The Mali international, 25, has attracted Sunderland, Wigan and Sheff Utd and also Ipswich with some eye-catching displays.
All the clubs were expected to make a deadline day swoop. on Thursday.
Sidibe, who has been offered a new deal at Preistfield, said "I really want to concentrate on keeping Gillingham up.
"I am not looking at the off-the-field issues, but purely at the on-field ones."
Sidibe has been playing upfront with former Sunderland man Darren Byfield recently.