The Toffees are expected to be one of the busier Premier League clubs on deadline day due to their need to bring in reinforcements.
New manager Sean Dyche wants to strengthen in several key areas of the squad but bringing in a striker is one of his and the club’s priorities.
Everton have been tracking several forwards over the course of the window and it has been claimed that Adams is one of the names on their shortlist.
The Merseyside club are interested in exploring a deal to take the Scotsman to Goodison Park on deadline day.
Dyche is believed to be keen on bringing in proven Premier League experience and Adams is a player he likes.
Everton are considering making an offer for him but they are likely to encounter an extremely reluctant seller in Southampton.
The Saints do not want to sell Adams to a relegation rival on deadline day as things stand.
Adams has started 17 of Southampton’s 20 Premier League games and Nathan Jones does not want to weaken his squad this late in the window with little time to source a replacement.