Llorente was released by Tottenham at the end of last season and the 34-year-old striker, who scored 13 goals across his two years in north London, has been heavily linked with United in recent weeks.
Solskjaer was desperate to overhaul his squad after a miserable end to the 2018/19 campaign, but only Harry Maguire, Aaron Wan-Bissaka and Daniel James arrived through the doors at Old Trafford before the transfer deadline, leaving the Norwegian short in central midfield and attack.
Alexis Sanchez will join Romelu Lukaku at Inter Milan in the coming hours and United have also lost Ander Herrera and Marouane Fellaini in midfield.
Paulo Dybala was strongly considered as a potential option, but United dropped their interest when it became clear the Argentine had major reservations about the transfer.
According to The Evening Standard, Solskjaer also pulled out of signing Llorente as he’s keen to avoid ’emergency’ moves and quick fixes which the club may live to regret.
Borussia Dortmund and England wonderkid Jadon Sancho remains United’s priority attacking target and Solskjaer is prepared to wait until next summer to get his man.
Earlier this month, Sancho signed a new contract with Dortmund which saw his salary jump up to £190,000-a-week.
Sporting director Michael Zorc branded Sancho ‘without doubt one of the most exciting players in Europe’ and stressed that the 19-year-old was settled at Dortmund.
‘At the moment, Jadon is very happy with us,’ Zorc told Bild.
After a miserable season with United, Lukaku scored on his competitive debut for Inter Milan against Lecce and Antonio Conte heaped praise on the ‘gentle giant’.
‘Lukaku stepped into the Inter world in the best possible way, with great humility,’ the Italian said.
‘He is a gentle giant, always has a smile on his face. He’s ready to work for the team and at the disposal of his team-mates.
‘I also want to highlight that Lautaro Martinez also played very well and everyone deserves praise today.
‘It was only the first game, so we can celebrate until midnight, but from 00.01 we have to start thinking about the next match with Cagliari.’