The 32-year-old returned to Southampton last year on a season-long loan from Everton and he has been a key part of the squad on the south coast.
His contract with Everton will expire at the end of the season and Walcott will be available on a free transfer in the summer.
And it has been claimed that Southampton are already working towards keeping the player at the club for the 2021/22 campaign and beyond.
The club are in conversations with the player and are hopeful of working out an agreement with him soon.
Ralph Hasenhuttl is happy with what he has seen of the veteran forward this season and wants him to be in his squad next season as well.
Walcott is also believed to be happy following his return to the south coast and is likely to agree to continue at Southampton.
He has scored twice and provided three assists for his team-mates in 17 Premier League appearances this season.
The attacker recently returned to action following a lengthy layoff from a hamstring injury.
