Sean Dyche’s side are trying to strengthen their squad in alignment with financial constraints this summer.
They have so far added three attackers, including Jack Harrison and Arnaut Danjuma, to their options in the ongoing transfer window.
Dyche is keen on bringing on more attacking reinforcements to Goodison Park and they have zeroed in the Saints star Adams.
The Toffees witnessed an initial bid worth £12m for the Scotland international rebuffed by the Championship outfit this summer.
The Merseyside club have made another improved offer for Adams and Russell Martin’s side have yet to accept the proposal, with talks over a £15m move stalled.
Now it is suggested that any potential deal for Adams is yet to be dead, albeit Martin is reluctant to let his star forward go in the ongoing transfer window.
Everton are also turning their attention to other targets as contingency plans and it remains to be seen whether they will continue their pursuit of the Scotland forward.
