Walcott's directness would add a lot to Southampton's game, while he managed to score 19 goals in 37 games across all competitions last season.
However, the possibility remains that Walcott could move move on during the current transfer window, with rumours of a move back to St. Mary's to join former club Southampton having gathered pace in the English media over recent weeks.
Arsene Wenger remains reluctant to allow Walcott to leave the club midway through the campaign, but the Gunners' striker is said to want to leave as he is keen to play regular first-team football.
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The 28-year-old has been tipped to call time on his 12-year career at the Emirates after falling down the pecking order this term, with just five substitute appearances to his credit in the Premier League.
Walcott looks certain to move either in January or in the summer transfer window.
Arsenal's English worldwide winger Theo Walcott has made a decision to leave the Gunners during this transfer window after having spent the first half of the season on the bench. This week however, according to the Evening Standard, the Saints have finally confirmed their interest in the winger.
Pellegrino told Sky Sports: "I have been talking about him". For us, it's not easy'.