Abraham is heavily linked with leaving Stamford Bridge this summer as he is down the pecking order in the Blues attack under Thomas Tuchel.
Chelsea are open to letting the striker go and have slapped a £40m price tag on his head, with Serie A outfit Atalanta along with Premier League rivals Arsenal and Southampton keen on him.
The Saints saw the departure of Danny Ings to Aston Villa on Wednesday and have enquired Chelsea about a loan deal for Abraham, but the Blues have made it clear they are only prepared to sell him.
Ex-Premier League star Mills is of the view that Southampton would have a good player on their hands if they can rope in Abraham, but stressed he believes the striker will have better options than the south coast outfit.
Mills suggested that Abraham should join a team that will be fighting for a place higher up the league table than Southampton, who could even be in a relegation battle next term.
While discussing Abraham’s immediate future, Mills told talkSPORT: “He would be a great signing for Southampton but would Tammy Abraham want to go there?
“That would be, not trying to be disrespectful, but I think Tammy Abraham would have better options than Southampton.
“Maybe go a little higher up the table, teams that are may be going to play more to his strengths.
“That would be the worry for Southampton because players will look at it and think, ‘okay, I am going to be in a relegation battle.”
It remains to be seen any of Abraham’s potential suitors in the likes of Arsenal, Atalanta or Southampton will be willing to stump up the asking price needed to snap him up in the coming weeks.
