Since taking over the reigns from Jose Mourinho, Solskjaer has led his former side to nine wins and one draw in 10 games across all competitions as he clawed them back in the top-four reckoning.
While the month of February will bode different challenges in the form of Paris Saint-Germain, Liverpool and Chelsea, many believe the general change in aura around the club makes the Norweigan the perfect candidate as the next full-time boss.
Rooney, the all-time record scorer of the English concedes it would be ideal for his former teammate to get the job, but offered an alternative should the club venture into a different direction, come end of the season.
"Ole Gunnar's a fantastic person," Rooney told CNN. "I think, the club will have a decision to make at the end of the season, and it'd be nice to see if Ole's going to continue with this form, and get a shot at the job on the payment basis.
"But if not, if the club go to choose from somewhere else, then I think in my opinion Pochettino would be the right guy."
The Premier League legend joined DC United last June and silenced many of his critics claiming his career was over with inspiring displays to lift off the bottom of the Eastern Conference and into the playoffs with 12 goals.
And this has led the 33-year-old to claim he could still perform at the highest level, despite English media dubbing his move to the US as a retirement switch.
"If I'm being honest, I know quality wise, I can still play in the Premier League. I know that. I've always been a confident person, and so I have high expectations of myself.
"And yeah, I've come here expecting to do well. And I think there was a surprise from people who have their opinions, which is fair enough, but I never doubted myself at all."