Rashford, 23, was replaced by Mason Greenwood after 73 minutes in Sunday’s derby victory over Manchester City with what appeared to be an ankle injury.
While he stopped short of ruling him out of the visit of the Rossoneri on Thursday, Solskjaer does not expect the England international to be ready in time, also suggesting he will be a doubt for the visit of West Ham United on Sunday.
‘I don’t think he’ll be available for tomorrow. He didn’t train today,’ Solskjaer told a press conference on Wednesday.
‘Normally [I’m] very optimistic but think he is out of tomorrow night and a doubt for the weekend.’
United could also be without Edinson Cavani for the visit of Milan.
The Uruguay international missed four games with a muscle injury in February before returning to the starting XI for a goalless draw with Crystal Palace on March 3.
The 34-year-old was sidelined again however for Sunday’s derby and Solskjaer is not expecting to have him back at his disposal.
‘I’m not sure if anyone will be back,’ Solskjaer continued.
‘David, no. Donny, no. Juan, no. Edinson, maybe. Rashford, no. Similar side to Sunday.’