Chelsea and Manchester United are also reportedly interesting in securing his services.
Dutch boss will seek to replace 33-year-old in the summer.
Nani has been a bit-part player at United since his arrival from Sporting Lisbon in 2007.
The England international underwent an operation in the United States on 5 May.
The Frenchman hints Walcott could be allowed to enter the final six months of his deal
The three-time World Cup winner was admitted to the Sao Paulo hospital on 5 May.
Jan Molby claims Liverpool's priority should be signing a goal scoring striker in the summer.
Reports had suggested Spurs were moving forward with a £9m offer.
PSV technical director Marcel Brands had recently revealed talks with Merseysiders over Depay.
Jenkinson has spent the season on loan at West Ham United.
Manchester United face Crystal Palace in the Premier League clash on Saturday. Find out how to follow the match live in the UK.
Jaap Stam believes Depay is perfectly suited to flourish at United under Van Gaal.
Manchester City are favourites to sign Roberto Firmino in the summer.
Rodgers is keen to sign a goalkeeper, who can challenge Mignolet on a consistent basis.
The Gunners are yet to register an offer but are expected to do so once the season ends.
Brendan Rodgers will hope that Sturridge can return fit following his rehabilitation post the hip surgery.
Liverpool and Chelsea are considering a move to sign Juventus' star midfielder Andrea Pirlo.
Louis van Gaal is keen to wrap up his summer signing ahead of United's pre-season tour of the United States.
Tottenham are considering a double move in signing striker Max Kruse and defender Kevin Wimmer.
Former Arsenal captain Adams understood to be handed a football role at club.
Depay will join United this summer after they and PSV agreed a move for the Dutch starlet.
Previously Daniel Levy and Franco Baldini have had a role in the club's transfer dealings.
The France midfielder has become a crucial asset in the boss line-up during the second part of the season.
What lies in store for the Ibrox club as it looks to re-enter Scotland's top tier?
Manchester United is also reportedly interested in securing his services.
The Argentine joked the Welshman could always rejoin Spurs if things don't work out.
The Wales midfielder continues to be hampered by a kick suffered against Hull.
The Argentine forward has been heavily linked with moves to the Premier League.
Former Newcastle star says Arsenal will challenge for the title next season.
The Dutch international admits 'many top clubs' were interested in acquiring him from PSV.