Redknapp had targeted signing the vastly-experienced Republic of Ireland international, who has just finished a campaign with the LA Galaxy in the US, in the new year on a short-term basis.
Keane, who counts Coventry, Leeds, Liverpool and Spurs among a long list of former clubs, is believed to be interested in a return to England on a short-term deal once again after a successful spell at Aston Villa 12 months ago, during which time he scored three goals in seven appearances.
Redknapp had hoped to sign the 32-year-old, who he knows well from his time at Spurs, when the transfer window reopens in January but now interest from Villa could hit the R’s chances of landing him.
Norwich, managed by Chris Hughton who also worked with Keane at Spurs, are also being linked with a January offer for the in-demand forward.
Napoli president Aurelio De Laurentiis has admitted there is a chance his club could lose the sought-after Maurizio Sarri this summer.
Chelsea roared back from two goals down to record a 3-2 victory at Southampton, with substitute Olivier Giroud scoring twice.
Coach Phillip Cocu insists his PSV side is ready to go into battle with Ajax on Sunday to claim another Eredivisie title.
Garry Monk is confident Birmingham have enough quality to survive in the Championship this season.
Atletico Madrid general manager Clemente Villaverde says there have been no talks with Barcelona on the sale of Antoine Griezmann.
Coach Jupp Heynckes insists Bayern Munich will not take their feet off the gas despite having already wrapped up the Bundesliga title.
Paris Saint-Germain are reportedly targeting Real Madrid striker Karim Benzema as a cheaper alternative to bolster their strikeforce.
Wolves boss Nuno Espirito Santo believes his side will face a tough test when struggling Birmingham visit Molineux on Sunday.
Huddersfield's Jonathan Hogg believes his side's chances of securing Premier League survival could hinge on their next two matches.
Bournemouth manager Eddie Howe is not about to hit the panic button as his side prepare to take on Liverpool and Manchester United.