The Potters have conceded four goals in their opening two Championship matches, meaning manager Gary Rowett may feel that an experienced defender is needed to bring solidity to the squad's rearguard.
Football Insider reports claim that a number of Championship clubs have eyed the 28-year-old with Stoke leading the race, as the Potters aim to secure the defender on a season-long loan deal.
Martina joined the Toffees on a free transfer from Southampton last season. The defender made 21 appearances for Everton, before losing his place following club veteran Seamus Coleman's return to fitness.
Cuco Martina being sent out on loan is confirmation that Marcel Brands is a magician.— Everton Fans Corner (@EFCFansCorner_) August 16, 2018
With the arrival at Goodison Park of new boss Marco Silva, Martina does not appear to be in contention for the Portuguese manager's squad. The captain of the Curaçao national football team has been training separately from the first-team, and the Premier League club would reportedly be happy to see him move on.
Martina can expect to be a vital player in Rowett's formation, as the 28-year-old can play anywhere across the backline and bring both experience and versatility to Stoke.
If the transfer is completed, Martina would be the second Everton player to join Stoke during this transfer market, following the arrival at the Britannia Stadium of Wales international Ashley Williams.