Asked about the Uruguayan's progress on Wednesday, Solskjaer said: "Edinson has done well in his rehab.
"We still have to make the decision if we should risk him. It is a little bit to risk him too early, I'd doubt him to be available to pick [against Sheffield United]."
Cavani has managed just 172 minutes of Premier League football since arriving at Old Trafford on a free transfer in early October.
He has, though, already netted on three occasions in English top-flight, including a crucial brace in a come-from-behind win over Southampton.
And, though the sample size of minutes played remains small, the signs are that the 33-year-old could have a bit impact for the Red Devils in the league this term.
He leads every one of his teammates in terms of shots per 90 thus far, having taken 4.7 on average since making his debut off the bench against Chelsea.
Only midfielder Bruno Fernandes gets close with 3.5, while Mason Greenwood (3.1), Marcus Rashford (2.4) and Anthony Martial (1.8) pail in comparison.
He is also ahead in terms of touches in the box, averaging 7.3 across 90 minutes in his one start and five substitute appearances thus far.
Of United's striking options, Martial comes closest with 7.1, while Rashford (5.3) and Greenwood (3.3) are some way behind.
Perhaps unsurprisingly given his deeper starting position, Fernandes trails in this metric, with 3.2 touches in the box per 90.
Furthermore, Cavani has even impressed creatively, laying on 0.5 big chances on average each match in the Premier League, with only Fernandes (0.8) ahead of that.
By comparison, Rashford (0.1), Martial (0) and Greenwood (0) do not stack up to the experienced former Paris Saint-Germain forward.
Cavani has a job on is hands to sustain this form as he starts to feature more regularly, but the early signs are that he deserves a chance to try as soon as he is fit.