The Sun says Gazidis is ready to speak with the England star's representatives - possibly in the next 48 hours - to end the contract deadlock.
Walcott, 23, who will see his current deal end this season, is set to be tempted with a £90,000-a-week salary over five years, bringing him level with top earners such as Lukas Podolski.
And he will also be offered a £3m signing-on fee to take the overall package to £26.4m.
Walcott and his team held unofficial talks with Gazidis early last month. But he has not had a concrete offer since the summer when he rejected £80,000 a week.
The player, who earns £50,000 a week, has seen his bargaining power increase due to recent goal-scoring displays in the new central striking role he craves.
He is also incredibly popular with the fans and is desperate to remain in north London.