Fryatt has found the net 22 times for the Foxes already this season, but is out of contract and able to leave on a free transfer in the summer.
"We are doing everything we can to sign him. We certainly don't want to lose him and in the next few days we will try to give it a go at reaching agreement," chairman Milan Mandaric told the Leicester Mercury.
"Matty has never suggested he wants to leave and he has been very positive and very bright. I would be very disappointed if we were not able to re-sign him and it should be a matter of a short time now."
Fryatt moved to Leicester from Walsall for an undisclosed fee in January 2006.