New Blues manager Thomas Tuchel wants Gilmour to stay at Stamford Bridge, with the teen star set to remain in the Blues' first-team squad.
Gilmour had feared being overlooked for first-team action under Tuchel's new Chelsea regime, and was open to a loan to boost his chances of making Scotland's senior squad for the summer's Euros.
Ex-Paris St Germain boss Tuchel rates Jorginho, Mateo Kovacic and N'Golo Kante very highly, and all three operate in similar roles to 19-year-old Gilmour.
Southampton had been keen to take Gilmour on loan, with West Ham having monitored the situation as well.
But now the former Rangers youth star is poised to stay put in west London, and will push for regular first-team action.
Scotland Under-21 midfielder Gilmour broke through under former boss Frank Lampard, impressing in a number of high-profile fixtures last season.
Gilmour had harboured concerns that Tuchel's arrival last week in replacing the sacked Lampard would halt his progress, and the highly-rated Scottish playmaker was omitted from Chelsea's first two matches under their new manager.
But German boss Tuchel has been impressed by Gilmour's work in training, and will look to involve him in regular first-team rotation.