McCarthy, 28, has not played a minute of competitive football for the Toffees since he suffered a double leg break against West Bromwich Albion last January.
He has also only been named in two matchday squads by manager Marco Silva this season, in the FA Cup win over Lincoln City on January 5 and the victory at Huddersfield Town on Tuesday, with his only football coming as a substitute in November’s friendly against Gor Mahia.
But his chances of first team football at Goodison could improve if fellow midfielder Idrissa Gueye completes his expected move to Paris Saint-Germain before the deadline.
Despite returning to training in September, Silva has, thus far, preferred Gueye, André Gomes, Morgan Schneiderlin and Tom Davies as his midfield options to McCarthy.
He has also been said to have interested a number of clubs this month, including Fulham, Newcastle United, West Bromwich Albion and Celtic.
Since joining the Blues in September 2013 from Wigan Athletic for £13 million, he has made 132 appearances for Everton, scoring six goals.