Scott McTominay is also set to undergo a fitness test to determine his availability after missing Wednesday's Manchester derby, while Solskjaer additionally stated that he plans to keep faith with star goalkeeper David de Gea, despite recent high profile errors.
"Ander has been training, he's been enthusiastic. He'll probably be involved. I think he's fit enough to be involved on Sunday. I can't guarantee it, because there's still two days left, but he's trained the last two days," the United boss said at his press conference, via ManUtd.com.
"I trust David and he's, for me, been the best player United have had in the last six or seven years," the Norwegian continued as questions moved on to De Gea.
"He's been absolutely outstanding and going through tough patches is just part of a footballer's career. David will be fine, no worries."
Ole on @D_DeGea: "I trust David and he's, for me, been the best player United have had the last six or seven years. He's been absolutely outstanding. Going through tough patches is just part of a footballer's career and David will be fine." #MUFC pic.twitter.com/Xe90kjJKM1— Manchester United (@ManUtd) April 26, 2019
Herrera's return to the United team to face Chelsea would be a huge boost. The fan favourite scored against Chelsea when United won at Stamford Bridge in the FA Cup earlier this season and has traditionally played well against the west London side, notably in a 2-1 win in 2017 when he scored and assisted, as well as marking Eden Hazard out of the game.
His future as a United player beyond the end of this season remains uncertain, though.
There were rumours earlier this month that Herrera had agreed a contract to join Paris Saint-Germain as a free agent in July. But it appeared that he hadn't actually signed anything and the lack of ink on paper was rumoured to have annoyed and worried PSG.
There was suddenly hope that he might be able to resolve his future with United after all and sign a new contract at Old Trafford. But RMC has now since reported that the PSG will be going ahead after seeing off late competition from Herrera's former club, Athletic Bilbao.
RMC reporting that #MUFC midfielder Ander Herrera has agreed a contract with PSG, with only the exact length of the deal (4 or 5 yrs) yet to be confirmed. Says there is 'no doubt' that free agent Herrera will join PSG this summer. https://t.co/Ed40FkjpKO— Jamie Spencer (@jamiespencer155) April 26, 2019
The French outlet stops short of saying that a deal has been signed, but claims there to be an agreement in place, with the exception of the length of the proposed contract.
Despite final details to be hammered out, RMC claims there is 'no doubt' that Herrera will join PSG.