Walker, who is currently a starter for City and won the treble last season, was at the Blades before moving on to Tottenham.
Asked about a possible Saudi Arabian move, he stated, per The Star: "I'm very close to Riyad (Mahrez, who left City for Al-Ahli last summer). He was one of my good friends when he was here. Listen, I'll never say never. The money they are paying is obviously a massive factor in why these players are going out there. I think for Ronaldo to go out there, he changed or he opened the pathway for everyone to go there.
"I think if they keep attracting the players that they're attracting, the league's going to get better. So then why wouldn't you want to go? But for me the Premier League is definitely the best league in the world, so I want to compete at this league for as long as possible for as high as possible before anything else. I've always said, as long as my legs are are going and I still feel that I can contribute at a certain level, then I want to contribute.
"I don't want to drop down too low because, no disrespect, but I feel the lower it gets, I think it gets harder. Certain things that you have the luxury of at City, whether facilities, nutrition, this, that or the other. But I'd like to finish at Sheffield United. That's something that I would actually like to do.
"I was there from such a young age until that until I went to Tottenham and I only played five (league) games before I went to Tottenham, and then went back on loan for half a season. So I think I've got like 35 games and I'd like to go for as long as possible, to give back or even pass on my experience to the younger players that are coming through or players that are there then. If I can do that, then I'd like to, yeah."