Reports says Spurs made an initial bid of just £6million for the England winger.
“I can confirm that we have received an offer from Spurs for Stewart Downing and I can also confirm that we have rejected that offer,” Gibson told the Daily Mirror.
“I’ve spoken to Daniel Levy and told him categorically that their interest is not welcome. I’ve also told him that we will not entertain any further offers for Stewart or, for that matter, any other senior member of our squad.
“The same applies to Tuncay and it also applies to Gary O’Neil.
“I repeat: none of our senior players will be leaving the Riverside Stadium this month. We’ve got a talented group of players and it’s time for us to knuckle down and focus on the job in hand.”