Swansea's Lukasz Fabianski has dismissed rumours of a move to Roma insisting he is happy in the Premier League.
Head coach Kenny Jackett has not given up hope of keeping Bakary Sako at Wolves beyond the end of the season.
Jack Wilshere, Alex Oxlade-Chamberlain, Kieran Gibbs, Carl Jenkinson and Aaron Ramsey have all signed long-term Arsenal contracts.
"We are delighted that these five young players have all signed new long-term contracts," manager Arsene Wenger said.
Liverpool and Manchester City are reported to be monitoring Walcott's situation with the England winger holding out for higher wages and a change in position to striker.
Walcott will have been encouraged by the quintet's decision to sign - especially Wilshere - and Wenger is pleased to have retained a British core within the team.
"The plan is to build a team around a strong basis of young players, in order to get them to develop their talent at the club," Wenger said.
"Jack is certainly the best known, the leader of this group - but the other four players are exceptional footballers, and we're very happy that we could conclude their new deals at the same time.
"I'm a strong believer in stability and I believe when you have a core of British players, it's always easier to keep them together and that's what we'll try to achieve going forward."
Wilshere, 20, has been in fine form since returning to action in October after 15 months out with ankle, foot and knee injuries.
Ramsey has made 24 appearances for Wales, who he also captained, while the other four are England internationals.