The Norwegian boss appeared to suggest after the New Year's Day defeat to Arsenal that Pogba's "people" had recommended the surgery, raising questions over how much input the club had in the decision, AFP reported.
Speculation continues to surround the 26-year-old French World Cup winner, who has been regularly linked with a move away from Old Trafford and whose agent, Mino Raiola, has been scathing about the club in comments made in the Italian media.
But Solskjaer was keen to play down any suggestion of a disagreement regarding the injury, and said, "Paul came back after a long spell out, (featured in) a few games, had a reaction, didn't go to Burnley.
"He felt his ankle was sore, we did a scan. It's not the same injury, it's a different injury. Of course when you get that scan you consult your own medical people as well, like I did. He wanted a second opinion and the advice was to have it done."
On the injury, Solskjaer added, "It's not a major one and probably, as I said, three or four weeks.
When asked again about why he had suggested it was Pogba's "people" behind the decision to undergo surgery, he added, "As in when you consult your surgeon and the ones you trust.
"That's maybe my bad English – you have people you trust and you speak to. When I had my injuries, knee operations, I had my people in Norway and Sweden that I spoke to and Paul obviously has people as well that he trusts, and that's important."
Solskjaer's team faces Wolves in the FA Cup third round at Molineux today, having been dumped out of the competition by the opponent in the quarterfinals last season.