Sako has had several injuries since arriving from Wolves on a free in 2015, appearing 39 times for the Eagles, 31 of which have been off the bench.
But after impressing during Palace’s striker crisis over the festive period, he has given manager Roy Hodgson another competent option up front.
His most recent exploits include a superb equaliser against Brighton in the FA Cup with his weaker right foot from outside the box.
When asked about whether he would like to stay, Sako said: "Yes, of course. Of course, of course,” speaking to the Croydon Advertiser.
"I am just enjoying my football at the moment, so I am not really focused on my contract situation.
"Fingers crossed I am injury-free now and I am enjoying my football.
"I was doing that before but I was just unlucky. I don't know why I was getting injured but now I am really happy."
Palace manager Roy Hodgson has converted Sako into a central striker as opposed to his original role on the wing. Sako had also been used as a central midfielder back when he played for Wolves.
But he attributes his newfound prowess to consistent game-time rather than his position switch.
"I am just playing regularly,
Completely changed my opinion on Bakary Sako, in recent weeks he’s been class. The one player to come out of last night with any credit.— Phil (@pnm1979) January 9, 2018
"I was happy with my performance at Brighton but unhappy we got knocked out as a team there.
"The manager here has been helping me a lot playing up front and I am now starting to get used to it.
"I still have to learn some things but I am trying do it right."