Allardyce has revealed that he wants to recruit the England international attacker from Premier League rivals Arsenal.
The former West Ham United and Newcastle United boss has outlined what he likes about the 28-year-old, who can operate as a forward or as a winger.
"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,” Allardyce told The Independent.
”Two or three reasons really - goalscoring threat, pace, experience and he's good on assists from wide areas in terms of his crossing ability.”
Allardyce added: "I don't think there's any chance of a loan so I think it is a permanent deal we're hoping to negotiate.”
Walcott started his professional club football career at Southampton and joined Arsenal in January 2006 for an initial transfer fee reported by BBC Sport to be worth £5 million.
According to The Sun, Arsenal want as much as £30m in order to part company with the England international.
The British tabloid has also credited Southampton and Newcastle United with interest in Walcott.
Walcott has a lot of pace and could make Everton more potent in attack, and his arrival would enhance the Toffees’ chances of finishing in the top eight of the Premier League this season.