The New Zealander was a standout performer in last season's campaign and won the club's player of the season award.
McKay joined up with Warriors ahead of the 2021/22 season and would qualify to represent Scotland in 2026 if he was to signs a new deal with thw club.
Speaking to Scotland Rugby News, McKay said: "I'd be keen to stick around but I need to go through the negotiations. But hopefully they are keen to keep me. The easiest thing for me to do is to focus on rugby and the rest will sort itself out."
On gaining eligibility for Scotland in 2026, McKay added: "I'm not on contract until then so I'd have to re-sign but I won't be eligible until that November."
McKay's contribution has been vital to Glasgow's recent success, especially with fellow full-back Ollie Smith out of action with a long-term ACL injury. McKay has played a lot of rugby over the past 12 months so with Smith nearing a return there will be renewed competition for the number 15 shirt.
McKay added: "If you asked any rugby player then obviously they'd want to play every week. Ollie has been working hard in the background and it will be awesome to see him back as it doesn't come much harder than an ACL rehab.
"It's definitely been a big blow for the squad but fortunately, I was able to stay injury free during that period. You want plenty of competition in the squad and everyone fighting for positions.'
For the next two weeks attention turns to the European Champions Cup starting against Sale and then Toulon before the 1872 Cup double-header against Edinburgh at the end of the year.
An agonising defeat to Harlequins put Glasgow out of last season's competition but McKay believes that was key to their URC success and the squad are determined to go at least one better this time around.
He said: "It was gutting to lose to them but it galvanised us as a group and it was after that defeat that we turned the dial and locked in to really believe. It would have been nice to go deep into Europe but it probably made us find out what we needed to do to win the URC.
"We've got a big belief in the squad about what we can do when we turn up with the right mindset. Time will tell because talk is cheap. There's no point talking about it and then losing. We've definitely got the belief but we need to go out and do it on the field.
"European footy is such an awesome time of year. A lot of people will circle this time of year on the calendar with the European games and the derby matches against Edinburgh. It's a pretty wicked time of the year to try to turn the dial."