The Republic of Ireland has been linked with a move away in the January transfer window, with him in need of game time ahead of Euro 2016 in the summer.
He has found game time hard to come by with the Blues this season, with him far down the pecking order in the first team squad.
However, despite interest from him from clubs in both the Premier League and the Championship, he now looks set to remain at Goodison Park.
It is unknown why a potential exit has fallen through at this moment in time, although perhaps manager Roberto Martinez is keen to use the midfielder in the second half of the campaign.
The Blues recently lost Muhamed Besic to injury and there is every chance that has influenced the Spaniard's thinking on Gibson's potential exit.
With the transfer window not set to shut until 11pm on Monday there is still plenty of time for things to turn around though, but for now it seems the midfielder will be remaining on Merseyside until the summer at least.