Blackburn owners Venky’s have backed Keane, but reports claim they could decide to axe the boss after taking just one point from the first four games of the season.
Solskjaer has managed to take Molde to the brink of the Norwegian league title after leaving his job as Manchester United reserves team boss.
Solskjaer’s agent, Jim Solbakken did not want to comment on a possible move to Blackburn.
“Blackburn Rovers have a manager,” Solskjaer’s agent, Jim Solbakken, told The Mirror. “And Ole is doing very well in Norway.”