The England midfielder signed a one-year deal last summer and will be able to walk out of the Lane on a Bosman free transfer at the end of the season. He is also allowed to speak to clubs in January.
Boss George has been delighted with Anderton since his arrival at Spurs two years ago and hopes he will re-sign again.
George said: “I am hoping Darren will be offered a contract at the end of this season. I don't deal with financial side of things so I am not sure what the situation is. The right time will come when we sit down with him. I don't want him to slip through our fingers.
“I want him to stay but, the way football works now, players can just say to the world: 'My contract is up at the end of the season, come and have a look at me'.
“He’s been very good in my time here. He very rarely misses training. He’s picked up a couple of injuries, a bad one last year with his Achilles, but he’s come back quickly to be fair to him.
“To be honest I’m surprised, with his talent, that no-one came in for him last summer. He is unbelievable on the ball.”
Anderton, 28, missed last weekend’s 3-3 draw against Bradford City with a one-match suspension after picking up five yellow cards. He is available again for Monday’s televised clash.
Listen to George's pre-match press conference in full by clicking here
George Graham welcomes Darren Anderton back for Monday’s derby against Arsenal with this message: I want you to stay.