But the centre back acknowledges that the reputation of the Clarets' Under 23s boss will have gone through the roof during his brief spell at the helm at Turf Moor.
The stand-in skipper, who was withdrawn with a tight hamstring during Saturday's defeat at home to Aston Villa, noted that the ex-Tranmere Rovers and Shrewsbury Town manager was 'obsessed with success' and was working around the clock in his mission to retain the club's Premier League status.
"He's obsessed with success," said Tarkowski. "I see the hours that he's putting in and the effort and the detail that he's going into. This is obviously a big opportunity for him to manage a Premier League team, which he's taken with both hands. He's done fantastically.
"I wouldn't know [if he's in line to get the job], I'm not too sure what the chairman's thinking is going forward. I think it was always just a short-term one at first to see how we did — I don't think the chairman expected us to be this successful so soon in the short period — so we'll see.
"He's done himself no harm; he got thrown in at the deep end one day and a few weeks later he's won three Premier League games. His stock has gone through the roof in recent weeks for what he's done with us because we were a team that had forgotten how to win football matches.
"To go and win three on the bounce shows how much change he's given us. We'll see what happens beyond the summer."
Tarkowski suggested that the mood has felt lighter since victories over Southampton, Wolves and Watford pulled the Clarets right back into contention for survival in the top flight.
There is still plenty of work to be done with games against Spurs, a return leg against Villa, and a home fixture versus Newcastle United all to be played before the season's completion.
"Wins change things," Tarkowski said. "If we'd have drawn those three then I don't think the mood would have felt so light. Wins on the board make it seem that way and it feels good when you're winning football matches.
"Everyone wants to be back in the building and ready to train again for the weekend. The wins definitely change it, but Jacko has done an excellent job in marginally changing the minor details, which has brought on our performances."