When Solskjaer took caretaker charge of United last December, Pochettino was favorite for the job, before the Norwegian's impressive run of results earned him the permanent role, Sky Sports News reported.
But with Pochettino no longer in a job after being "relieved of his duties" by Spurs on Tuesday, speculation about a potential move to Old Trafford has intensified.
"It doesn't bother me at all. I've got the best job in the world," said Solskjaer ahead of Sunday's trip to Sheffield United.
"If you're in a job, or if you're out of a job and you're a manager, you want this job. It doesn't really matter whatever happens around. I've got to focus on my job at Manchester United and do it as well as I can.
"I speak with Ed Woodward and the owners all the time about how we're going to move the club forward. That doesn't change if some other clubs change their managers."
'Jose return a circus’
Spurs appointed former United manager Jose Mourinho on Wednesday, less than 12 hours after sacking Pochettino.
United midfielder Nemanja Matic, who has been signed by Mourinho twice in his career, liked and commented on an Instagram post suggesting he was waiting for the Portuguese to bring him to Spurs in January.
"When it's like this, you like Jose coming back," added Solskjaer.
"It's going to be a spectacle and a circus and Nemanja has a sense of humor."