The FC Twente 'keeper has had an impressive season in Holland, performing well in the Champions League and cementing his position as number one.
He has had previous in the Premier Leauge, having signed for Liverpool in 2007, but he has matured greatly since making his loan switch to Twente permanently and, at only 24 years of age, he still has his best years ahead of him.
His form has attracted the attention of many clubs but Fulham were one of few to express a genuine interest during the January transfer window. He was being pursued alongside Roma goalkeeper Marteen Stekelenburg but, in the end, neither deal materialised.
Schwarzer, still number one at Craven Cottage, has performed admirably in the meantime but that hasn't stopped Jol's pursuit of a new, top-class 'keeper. And Mihaylov fits the bill.
"There are more clubs interested than just Fulham," Mihaylov told Dutch paper De Telegraaf.
"However, at the moment I want to focus fully on my job at Twente."
But what does it all mean for Schwarzer, who has made no secret of his desire to play well into his forties? The signs are, palpably, not good, but if his form and fitness don't dip, perhaps Jol would be tempted to stick with what he has got.
That would benefit the Australian, undoubtedly, but in the long run, the club could lose out without investment in a fresh number one. Beyond Schwarzer there is David Stockdale who, while intermittently proving his worth to Fulham, hasn't won the faith of our Dutch manager. And that is all that matters.
So, perhaps there is a valid argument to Jol's steadfast hunt for a new shot stopper. It's just that, inevitably, someone will miss out.