Jack Sullivan, the son of West Ham United co-owner David, has taken to Twitter to deny the club's interest Liverpool star.
Aston Villa are reportedly interested in signing Norwich City winger Robbie Brady.
Ibrox side Glasgow Rangers look on the brink of signing another big-name player.
The young goalkeeper has been released after two years at Goodison Park.
The 20-year-old Tottenham Hotspur target once turned down the Arsenal boss, according to reports.
Manchester City are also claimed to be keen.
This game was approaching half-time when the ball looped up invitingly from the mess of bodies in the Slovakia penalty area to the Englishman loitering on the edge of the box.
The England manager claimed otherwise but he needed to secure top spot in Group B and a performance that demonstrated strength in depth to justify six changes from the team that defeated Wales.
Chris Coleman savoured the best moment of his career as Wales emphatically defeated Russia to finish top of Group B and set up a last 16-tie in Paris on Saturday.
Roy Hodgson did not really want to leave the pitch at the end here. He paused and looked around the Stade Geoffroy-Guichard. He waved vaguely at the emptying stands. He strode across to shake Joe Hart’s hand as England’s last player left the pitch. In the end there was nothing left to do. Hodgson walked off, quite slowly.