Jan 14, 2018, 0:04
The 28-year-old forward has not started a Premier League game for the Gunners since last April and looks to have no future in North London.
The Toffees boss said that Walcott will bring pace and quality along with a goalscoring threat, and also will be a great addition to the squad.
The links to Walcott in the press have grown in recent weeks and Allardyce admitted in his pre-match press conference that he would love to bring the England worldwide to Goodison Park this month.
"If that is at all possible it would be very nice, but it is not imminent at the moment but some negotiations are going on".
"I think a lot of people would say that he's not really fulfilled his potential that we expected him to go on and achieve in the game at Arsenal Football Club".
Walcott was in the Gunners line-up for Sunday's FACup defeat at Nottingham Forest but has not started a PremierLeague match all season.
"Theo went to the World Cup in Germany in 2006 and we are now in 2018 and since he has not been for different reasons, so that is a sensitive subject".
Wenger said on Friday: "Jack [Wilshere] was injured but we had very good news yesterday morning".
"You don't get optimistic because so many things can happen in such a short space of time".
However, Arsenal are in no rush to reach a decision over Walcott and according to the BBC, the club want to assess the injury situation in their squad before taking a call on the England global.
'You can not give this [assurances] because it's not honest.
Asked if the move was motivated by Walcott's worldwide ambitions, Wenger said: "Yeah of course, everyone wants to play".
"Because Arsenal have got to find what we are losing at the moment".
Davis, Rondo power Pelicans past Spurs, 122-98
76ers rally late, push Heat to brink of elimination
An opposition fan's thoughts on the upcoming FA Cup clash
Wenger's legacy at Arsenal 'untouchable' - Henry
Israeli troops fire at Gaza protests; 9 wounded