Derby manager Rooney was one of the names cited as a possible option for Burnley after the Premier League club sensationally sacked long-time boss Sean Dyche on Friday.
Dyche had overseen 425 matches in charge of the Clarets, including 258 in the Premier League. Only six other managers have taken in more games with a single club in the competition.
At nine years and 167 days, Dyche's tenure was the longest among Premier League coaches prior to his dismissal; Jurgen Klopp's Liverpool reign (six years and 189 days as of Friday) was a distant second.
Dyche leaves Burnley 18th in the top flight and four points from safety with eight games remaining, leaving little time to hire a replacement.
Burnley Under-23s coach Mike Jackson, supported by a staff including injured captain Ben Mee, will lead the first team at West Ham United on Monday (AEST), but Sam Allardyce has been linked with the post – along with Rooney.
The former Manchester United and England captain was also reported to be a candidate for boyhood club Everton before it appointed Frank Lampard, yet he remains for now at Derby, attempting to beat relegation from the Championship.
"I think it's a compliment to me and the staff, what we've been trying to do here," Rooney said after a 2-1 win over league-leading Fulham on Saturday (AEST). "[It was] the same with Everton, when you get linked with Premier League clubs.
"I was surprised when I saw that Sean Dyche had been sacked, he's been brilliant for Burnley over the last 10 years.
"Obviously, I've seen the links, I've seen in the news, various news articles that I've been linked.
"But for me what's important is I focus on trying to keep this club in this division. And the future, my future depends on this takeover, that needs to be completed."