The right back's current deal is set to run out next summer and he has recently claimed the club are yet to inform him of what they plan to do about the situation.
With a number of sides said to be interested in making a January move for the former Premier League winner, Leicester may look to earn themselves a transfer fee in the next window before the defender is available to leave for free.
The Daily Mail report that Simpson would prefer to stay
The 31-year-old has struggled for game time this season and was made to wait until November for his first appearance. He has now, however, featured five times in the league and came on to sure up the defence in the impressive recent win over Manchester City on Boxing Day.
Speaking of the contract situation, Simpson stated: "Obviously my contract is up at the end of the season. It's kind of out of my hands really. I'm pretty sure at some point people in charge will speak to me."
Simpson elaborated on his thoughts in an optimistic tone, explaining: "
"I love it here. I'm happy at the club, the fans, everything. There are lads who have left this place who miss it.
Source : 90min