Leicester had made three bids for the Robins star striker but Bristol held firm against their Championship rivals.
Sexstone told the club's official website: "Leicester were very determined and they were pushing very hard.
"They did submit a fourth bid, a very substantial bid, far in excess of what they had offered before.
"It was a lot of money but the board was adamant that we want to keep Nicky Maynard.
"We will continue to work on getting him signing a new contract but in any event we didn't want to be selling to another Championship club."