Walcott, 28, has only appeared in five league matches this season, with this lack of game time having attracted the attention of his former club, who have funds after the sale of Virgil van Dijk to Liverpool for £75 million.
Walcott, who signed for Arsenal from Southampton as a 16-year-old in 2006, has found first-team opportunities hard to come by at the Emirates this season.
Walcott was handed a start in the FA Cup on Sunday, but looked out of sorts as the holders crashed out against Nottingham Forest.
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However, Walcott's former side could struggle to bring the England worldwide back to the south coast due to his hefty £110,000 a week wages, allowing Everton to take the lead in the race for his signature, according to the Daily Mail.
Walcott would face a hard decision if Arsenal were to accept a bid, as he has a young family in the south, so may choose Southampton and take a pay-cut to join the Saints.
Walcott scored 19 goals in all competitions previous year, and this season he has produced three goals and five assists in five UEFA Europa League appearances.
Southampton will try to negotiate with Arsenal over the signing of Theo Walcott during the January transfer window, according to the Daily Mail.