Maynard, whose contract expires over the summer, was recently put on the transfer list after he refused a new deal.
Swansea City, West Bromwich Albion and Wolverhampton Wanderers are among the club thought to be interested in the 25-year-old.
"I don't understand all this talk about Maynard," said McInnes after his side's 1-0 FA Cup defeat at Crawley Town.
"He's a Bristol City player, we paid for him and we pay his wages. All the while that's the case, he will continue to play for us."
Bristol City continue their Championship campaign on Saturday with a trip to Brighton & Hove Albion.