Theo Walcott celebrates for Arsenal
West Ham were as short as 7/4 just last week, but their odds have drifted out while Leicester's have been reduced.
Arsenal's Theo Walcott in action with Sunderland's Lee Cattermole
If Leicester were to make a move for the 27-year-old, it would turn the tables on the Gunners, who have pursued their players this summer.
Arsenal attempted to sign Jamie Vardy, activating his release clause, only for the talisman to reject the move and sign a new contract with Leicester.
Riyad Mahrez celebrates after scoring the first goal for Leicester
In recent days they have been linked to Riyad Mahrez, the reigning PFA Player of the Year, with Eurosport France suggesting a deal could be close.
Mahrez signing for Arsenal would limit Walcott's chances of a regular first team role, having spent the latter part of last season on the bench and missing out on England's Euro 2016 squad.
One possibility could be that the two clubs engineer a player plus cash swap deal with Walcott and Mahrez switching clubs - and there are not many Arsenal fans who would prefer to keep the former Southampton prospect instead of signing Leicester's Algerian star.
Leicester's Riyad Mahrez