The football world seems to move faster and faster these days. No sooner had the World Cup ended than attention immediately shifted to the transfer market - which is understandable, given some massive deals are expected to be confirmed in the coming days, following in the footsteps of Morgan Rogers' shock £117 million move from Aston Villa to Chelsea.

Of course, we've already seen some expensive signings since the summer window opened in the middle of June, with Rogers' England team-mates, Elliot Anderson and Anthony Gordon, joining Manchester City and Barcelona, respectively, for huge fees.

So, with just six weeks to go before deadline day, where do Europe's elite presently stand? Which teams have already done the majority of the business? And who still has an awful lot of work to do before September 1?

Arsenal

Arsenal haven't been inactive. Piero Hincapie's loan move from Bayer Leverkusen has been made permanent - and for a bargain £34.5m - while Illan Meslier has joined on a free transfer to add depth to the goalkeeping department. There have also been a number of exits, the most notable of which is Leandro Trossard, who has joined Besiktas for £17m, with Club Brugge's Christos Tzolis expected to arrive and fill the Belgian's role in the squad.

However, Arsenal supporters are nonetheless getting a little antsy. They expected a big-money arrival by this stage, but they're still waiting for a significant signing, after seeing their side refuse to meet Aston Villa's extortionate asking price for Rogers, while it's also been reported that the Gunners thought Bruno Guimaraes would be available for a lot less than the nine-figure fee Newcastle are demanding.

What's more, even though Julian Alvarez, a player that Mikel Arteta greatly admires, has gone public with his desire to leave Atletico Madrid, the Argentine reportedly has his heart set on a move to Barcelona. And even if the Rojiblancos would probably be much more willing to let him move to north London, they're still going to demand a gargantuan fee for the forward.

Arsenal, then, are in a very delicate situation. They want to build from a position of strength, having just been crowned champions of England for the first time in 22 years, but they're unwilling to pay over the odds for their transfer targets.

What happens next is unclear, but what we do know is that Arsenal could really do with a dominant, ball-playing midfielder, a top-class left winger and more quality cover in the centre of defence after losing William Saliba to injury.

Grade: D-

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Barcelona

Just like Thomas Tuchel, Barcelona effectively had to choose between Marcus Rashford and Gordon this summer, and, just like the England boss, they ended up going with the latter. Whether that was the right call for the Blaugrana is open to debate.

Gordon is younger than Rashford, but he was more than twice as expensive, even though he's not really a superior player. Still, Gordon showed enough at the World Cup to suggest that he has the kind of pace and versatility required to make a similar impact at Barca to Rashford, who contributed 14 goals and as many assists to the Catalans' cause last season.

Barca do still, however, have a gaping hole to fill up front, with Robert Lewandowski having brought the curtain down on his goal-laden spell in Spain.Deco's dream replacement is Alvarez, but it's going to take something close to a world-record fee to even get Atletico Madrid to the negotiating table.

Consequently, cheaper options are being explored, even if someone like Eli Junior Kroupi (also a reported Tottenham target) would still probably cost around £100m all-in. Do not be surprised then, if Barca, have a rummage around in the bargain basement, especially as Spain's World Cup hero Ferran Torres might also move on soon, given he has just one year left on a contract he seems highly unlikely to extend.

Looking elsewhere, Barca are well-stocked in midfield and may even look to generate some pure profit by cashing in on Marc Casado, and any money raised would likely go towards a dominant centre-back to play alongside the prodigiously gifted Pau Cubarsi - or perhaps even a new full-back.

Grade: D

Bayern Munich

It's already been a pretty positive window for Bayern Munich, who confirmed deals for both Ismael Saibari and Nathaniel Brown while the World Cup was still going on.

The Saibari deal had effectively been done before the tournament began, which is just as well really. The versatile Morocco attacker had a terrific tournament, and €50m looks like a terrific bit of business by the Bavarians. Of course, Brown's arrival means that Vincent Kompany won't have any concerns at left-back this season, even if Alphonso Davies decides to depart.

There's still talk that Bayern will look to bring in further reinforcements in centre midfield and right-back, but their main concerns at the moment are convincing Harry Kane to sign a new contract, and fending off interest from Real Madrid in Michael Olise, who is rumoured to be keen on linking up with France team-mate Kylian Mbappe at the Bernabeu.

How those two situations resolve themselves will define Bayern's window. For now, though, it's a case of so far, so good...

Grade: B