The 22-year old Frenchman spent last season on loan with the Scottish club and was a key contributor, making 31 appearances and impressing many along the way.
Sissoko indicates that he is favouring a permanent return to Rugby Park but feels that Udinese are pricing him out of a move.
"I know Kilmarnock would like to keep me, but I'm not sure it is going to happen because my club are asking for a lot of money," said Sissoko in the Daily Record.
"I'd be interested in staying in Scotland. I'd like to look at all my options, but at the moment I can't do anything because of the fee.
"It's down to my club, but I doubt Kilmarnock would be able to pay that. I don't have any other offers, so I don't know where I'll be playing."
It is understood that Udinese want a fee of around £750,000 for the former Celano, Gallipoli and Eupen loanee which Killie are unlikely to be able to afford.