The 28-year-old’s Arsenal contract does not run out until 2019 but he has made just 15 appearances this season and has yet to make a Premier League start.
“I think you are all aware of our interest in Theo,” said Everton boss Sam Allardyce.
“If that is possible to get over the line I’d be delighted.
“Obviously there are negotiations that are happening at the moment and if that can all be sorted out one of the most difficult things to do today – then that would be a great addition in my opinion to come and join us from an attacking point of view.
“Two or three reasons really – goalscoring threat, pace, experience and he’s good on assists from wide areas in terms of his crossing ability.
“If that is at all possible it would be very nice. It is not imminent at the moment but some negotiations are going on.
“I don’t think there’s any chance of a loan so I think it is a permanent deal we’re hoping to negotiate.”