Sporting are demanding 80m euros (£68m) for the 25-year-old, which United are unwilling to pay.
Talks continue between the clubs for a player rated at 45m euros by Tottenham Hotspur last summer.
United have not ruled out targeting alternatives having made a priority of looking at midfield options this month.
However, they will only look at existing targets and with two weeks remaining before the transfer window closes, Fernandes remains their first choice.
United have told Sporting a deal will not be done unless they drop the fee.
Solskjaer and his assistant Mike Phelan watched Fernandes play against FC Porto on 5 January.
United take on leaders Liverpool at Anfield in the Premier League on Sunday (16:30 GMT kick-off).