Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
Former Rovers centre-back Hendry was brought onto the club's coaching staff by now-departed boss Steve Kean in the summer.
The 46-year-old remains at Ewood Park working under caretaker-boss Eric Black, who he feels would be ideally suited to the role on a permanent basis.
When asked by TalkSport if he was interested in becoming Blackburn's manager, Hendry said: "No, not at all. I'm very lucky in what I'm doing, being back at the club that I love. I've been out of the game for five years.
"When you are looking at candidates for this position I don't think you need to look any further than the man in charge at the moment, Eric Black. He's got all the boxes ticked, that's for sure.
"If it's a bit of experience that they need to go and look for I agree with that. I don't think it (should be) anything but an experienced man. But I'm enjoying working for the football club in my capacity at the moment."
Oldham boss Paul Dickov has also brushed off reports marking him out as a surprise contender.
Reports claimed Dickov and former Rovers team-mate Garry Flitcroft had emerged as leading candidates as the npower Championship club's hierarchy prepares to draw up their shortlist.
Dickov, who is in his third season at the helm at Boundary Park, suggested the speculation might be a result of his presence at Blackburn's Brockhall training complex on Wednesday for a reserve game between the two clubs.
However, he dismissed talk of a move to Ewood Park, claiming: "That's the first I've heard of it. Maybe they've put two and two together and got five because I was at Brockhall, I don't know."