Sporting captain Fernandes was said to be a United target in pre-season, but no move materialised and he ended up signing a new contract in November.
But that new deal has not stopped fresh speculation this month, United reported to be the frontrunners in the race for Fernandes, a Portugal international.
Sporting's demands differ between the various media reports, however they claim United are likely to have to pay in the region of £60million (€70m) for the attacking midfielder, while some stories claim Marcos Rojo could return to Sporting as part of the deal.
But Solskjaer insisted there was nothing new to tell.
"I've got no transfer updates, so no," said Solskjaer when asked if he could provide an update on the apparent pursuit of Fernandes.
"If we get something that we can tell you about we will, but I've got no news now."
But Solskjaer reiterated that United have the capability – and he has the backing – to enter the market if they wish, as he moved to downplay the importance of Deloitte claiming the Red Devils are at risk of losing their status as the Premier League's highest revenue-generating club for the first time next year.
"For me, the most important thing is we get the results sorted, the performances on the pitch," he said.
"That's got to be my focus, but I know we've got the resources and the backing if we've got to go into the transfer market, for example. We're still up there aren't we? So, we're still in a good place."
Speculation around Ashley Young's apparent move to Inter has gone quiet in recent days, though he remains out of contention for United's FA Cup third-round replay against Wolves on Wednesday.
"He's not going to be involved," Solskjaer said of the versatile 34-year-old.