The national stadium has hosted three NFL games in the past two months, as well as England's comfortable Group E victory over San Marino.
England manager Roy Hodgson raised concerns that the Jacksonville Jaguars' clash with the Dallas Cowboys on the weekend had been scheduled too close to the Slovenia clash - and he will have looked on in dismay as the pitch was cut up during the Cowboys' 31-17 win.
He said: "I'm pragmatic and this match has been organised for a period of time now. The pitch, unfortunately, is not in the best of nick, which we're all a bit unhappy with. I think it will get put right."
Wembley Stadium's managing director Roger Maslin has claimed the damaged turf has been caused by a renovation in the British summer rather than any additional damage by the visiting American footballers, but concedes it is unlikely to be in top condition for England's match on Saturday.
He told the Football Association's official website: "We strive to deliver the best possible surface, so I'm slightly disappointed that the surface isn't as good as it should be but I'm confident it will be back to its pristine state after a winter renovation.
"We absolutely can [manage a busy calendar]. This isn't so much a problem of the NFL but of our summer renovation
"Whether it's the England team - which is absolutely at the core of the stadium - or whether it's Rugby World Cup, NFL, Saracens or Rugby League, I am very confident we can deliver a fantastic surface for all those event owners.
"Roy is totally entitled to his opinion. We have a very good working relationship with the England team and we'll be working closely with them this week to ensure we deliver the best possible playing surface for the game on Saturday.
"I met Roy at the end of last week and no doubt we'll pick up with the team on Thursday and Friday this week too."
