A host of British clubs are interested in signing Roy Keane after his shock departure from Manchester United.
Celtic are the favourites to sign the 34-year-old, but Portsmouth, Wigan and Bolton are also interested.
"Milan Mandaric believes he is the kind of character the club would welcome," read a statement from Pompey.
But Spurs coach Martin Jol has ruled out a move while Everton boss David Moyes declined to comment on Keane after Saturday's defeat to West Brom.
Jol told BBC Radio Five Live that although he admired Keane, he did not need to strengthen his team in that area.
"It's against everything we believe, we have very good players in that area," Jol said.
"Carrick is on the fringe of the England team, I have Jermain Jenas, Edgar Davids, I can play Pedro Mendes there - I think we're just fine in that area."
Wigan audaciously tried to sign Michael Owen in the summer before the England striker moved to Newcastle from Real Madrid.
Then the new promoted club were favourites to be relegated, but after a storming start to the Premiership, chairman Dave Whelan believes Wigan could be an attractive proposition for the midfielder.
"If Paul Jewell came to me and said to me can we go and sign Roy Keane I'll back him," Whelan told BBC Radio Five Live.
"They all say he will go to Celtic, but let's wait and see."
A potential stumbling block for the three English clubs is that Keane has previously said he would find it "hard to stomach" playing for another Premiership club.
Bolton boss Sam Allardyce also admitted Keane's wage demands for Bolton could be prohibitive.
Whichever club Keane joins he will not be able to make his debut for them until 1 January.
Although Keane's United contract was cancelled "by mutual consent", Fifa rules stipulate that no player subject to such a move would be allowed to sign for a new club outside the next available transfer window.
Meanwhile, a report in the Sunday Times claimed an unnamed Serie A club wants to bring Keane to Italy.