Walcott, 28, has struggled to hold down a place in the Arsenal first team and has seen only 47 minutes of action in the Premier League this season.
Speaking after Southampton's 1-0 win over Fulham in the third round of the FA Cup, Pellegrino confirmed that Walcott was among the players he was looking at but added that signing the England international could prove to be a difficult task.
Southampton have money to invest in the transfer market following the world-record £75m ($102m) sale of Virgil van Dijk to Liverpool.
"I have been talking about [Walcott]," Pellegrino was quoted as saying by Press Association. "He is a good player, but I don't know with the negotiations, with the market. I imagine that this type of player would have a lot of possibility. For us it's not easy.
"Hopefully we can bring somebody that can help us be stronger. This is our target now. We know the market is difficult, but we are working on that."
Walcott left Southampton's academy at the age of 16 to join Arsenal in a £12m transfer in 2006. He is the Gunners' longest-serving player with 395 appearances under his belt.
The 28-year-old has 18 months left on his Arsenal contract, with manager Arsene Wenger saying last week that he wanted the forward to stay at the Emirates Stadium.
"I want him to stay," Wenger was reported as saying by the Daily Mirror on 5 January. "I heard about [rumours linking Walcott with Southampton] but I want him to stay."
All of Walcott's starts for Arsenal this season have come exclusively in the Carabao Cup and the Europa League.
Everton and Newcastle have also been linked with moves for the England forward, who netted 19 times for Arsenal last season.