Begging for Keane: Neil Lennon
Tottenham will have first call on their player come the end of the season, while former Celtic manager Martin O'Neill is understood to be keen on snaffling the 29-year-old Irishman for Aston Villa.
With the player himself remaining resolutely non-committal, Lennon has declared his intention to continue 'hammering away' at a deal that would delight supporters and also shift season tickets.
'I'm not giving up on him staying,' Lennon said. 'I will be begging him every day from here on in to stay if he can.
'We need that calibre of player at a club like this. His pedigree and his record speaks for itself.'
Keane's wages of £65,000 per week are the most obvious hurdle, even if another loan deal removed the need for a transfer fee, and Lennon himself admitted that the final decision on finances would rest at boardroom level.
But the caretaker boss is clearly keen to put pressure on the Parkhead money men.Asked if the club could afford Keane, Lennon said: 'I think so, yes. You'd have to ask the powers-that-be.
'Would he be worth it? I'd say yes. He's only 29. I came here at 29 and played until I was 36. There's no reason why you couldn't get five or six years out of him. He is still at his peak.
'I know he's had a wee problem with his knee but we've been able to manage that over the past few weeks. He's trained the last couple of days and looked great.
'I wouldn't rule anything out. Ultimately, it will be Robbie's decision, whether he wants to stay or go. We will just keep hammering away at him.
'The more positive results, if we're playing well, the more we might be able to turn his head. We'll try to convince him.
'He's a world-class player, he loves the club, he has shown that in the time he has been here. We'd love to have him.
'It might be a lost cause but you never say never. Until we get a definitive no, then I don't see any reason not to keep trying.
'These last three or four months have given him a look at Scotland, given him a look at the environment, a look at the club, a look at the players.
On target: Robbie Keane scores against Kilmarnock
'He will know in his own mind what he wants to do. If he wants to go back to England, then there might not be a lot we can do.'
Anyone looking for a clue as to his intentions from Keane will struggle. The prolific scorer who has banged in a dozen goals in as many games for his temporary employers said yesterday: 'Who knows? No one has said yes or no.
'We said at the start I would just enjoy my football and concentrate on that, with no contract talk until the summer. I've enjoyed it here, of course, playing for a fantasticclub. There have been a few ups and downs, but that's the way it goes in football.
'I would like to think I have contributed in a small way to the team doing OK. We would have liked to have done a lot better, but that hasn't been the case.
'I'm not saying there is a chance or that there isn't a chance. I'm just saying that when I came here, we said we would speak at the end of the season if there was an opportunity to do so. In football, you never know.'
JUNINHO VIDEO SPECIAL: As the Middlesbrough legend retires - Sportsmail relive his finest momentsCeltic boss Neil Lennon Keane on keeping Robbie at Parkhead next seasonEXCLUSIVE: Larsson rules out Parkhead post: 'Give it to Lennon'Henrik Larsson on the appointment fit for a king: Swede offers his blessingCELTIC FC