The Toffees' England international defender has been strongly linked with a move to Arsenal, with one approach from the Gunners having already been knocked back.
Arsene Wenger is reported to be mulling over a second bid, with a new centre-half top of the Frenchman's wish list.
Everton, though, are determined to retain the services of their key men and will not part with Jagielka without a fight.
Distin believes the Toffees will come out on top in that tussle, with his defensive colleague having offered no indication that he is looking to leave Goodison Park.
He said: "He's not come out and said he wants to go anywhere, so I guess that means Jags wants to stay.
"It's still a club to be at. I don't think any players want to leave here to be honest. My guess is he's fine here.
"I haven't told him not to go - there's no point doing that. If he comes to me and asks, I'll tell him what I think, but it's not happened so we're happy he's staying.
"He's an amazing player, you don't play for your country if not. He's still young and still improving.
"He had some injury problems but seems to be over them now and is doing great - he's quality. The fact top clubs are after him is a sign of his quality."