The 41-year-old Leven has had two spells as Aberdeen caretaker since joining the Pittodrie coaching staff in June last year.
The former Kilmarnock, MK Dons and Oxford midfielder was also assistant manager at Kilmarnock, Dynamo Brest and Russian side Orenburg before his move to Pittodrie.
“It’s up to him, but so far so good, he’s focusing here for the game tomorrow,” Thelin said. “It’s always a blow when you lose staff. We’d miss him, of course.
“When good people do good things, they get eyes on them. We want him to stay here, but it’s also good that he gets recognition from other clubs as well.”
Aberdeen midfielder Leighton Clarkson added “we’d all be gutted to lose him”, given “what he’s done with a lot of the players when he was interim manager and what he’s doing now”.
“He’s a big character and a big coach,” he said. “His knowledge of the game is really good, the way he wants to play football and the way he communicates with all the lads is good and he’s the one who does all the extra sessions and he’s been a big part of my journey.”
Friday’s away victory took Lynch’s side to within three points of Northern Ireland Premiership leaders Linfield with a game in hand.
The Belfast-born 44-year-old, who was previously assistant at Glentoran, has been in charge since 2017 but has caught the eye after back-to-back titles and progress to the Conference League to become the first Northern Irish club to reach the main draw of a European competition.
Ayr United’s Scott Brown had been linked with the job at McDiarmid Park, but the former Celtic and Scotland midfielder has since signed a contract extension with the Scottish Championship club.
Celtic manager Brendan Rodgers suggested it was “no surprise he didn’t take it”.
“Scott’s doing a fantastic job at Ayr and, I think, for Scott, there’s no rush,” he said of the former Fleetwood Town boss. “You know, I’ve got no doubt he’ll be a really successful manager. He’s at a good club and and he’s happy.”
Former Northern Ireland striker Kirk and assistant Alex Cleland will take charge of St Johnstone for a second time as Premiership leaders Celtic visit on Saturday, having drawn their first game 3-3 at Ross County last weekend.