Arsenal manager Arsene Wenger says he is now "99 per cent certain" a new deal with the forward will be signed this week.
The England player would have been a free agent at the end of the season.
It is thought the deal extension would make Walcott among the highest-paid players at the club worth close to £100,000-a-week.
"I was scared at some stage, yes, that he could leave because it is like that with the experience I have in negotiations," Wenger said at a press conference ahead of the Premier League game at Chelsea on Sunday.
Wenger has developed the player from a raw talent after bringing him in from Southampton seven years ago.