Izzet staying with Leicester
Blackburn Rovers made a bid for the former Chelsea man during the transfer window while Aston Villa were also reportedly keen on the midfielder.
Despite Izzet having just six months remaining on his current deal, he will be staying at the Walkers Stadium until the end of the season.
"The situation with Muzzy is he is going to stay until the end of the season when his contract runs out," said Bassett. "A few clubs did enquire about Muzzy.
"We sat down about a week ago and pointed out if he really wanted to leave us to go and talk to these clubs.
"But Muzzy's a Leicester boy. He got relegated with us and wanted to make sure Leicester stay in the Premiership and felt the circumstances weren't right.
"He's not going to stay if we get relegated, but we've assured him we'd like him to stay if we do stay up."
Meanwhile, Peter Canero is travelling to Leicester and Bassett believes the defender will prove a great long-term signing for The Foxes.
"Peter's been recommended to us by a lad we know in Scotland who's looked at him probably for about a year," he added.
"We'll get things moving. He fits into our system, he's a young lad with potential to improve.
"We've agreed a fee with Kilmarnock. The boy's travelling down today and we can get him sorted out."