The defender impressed during a season-long loan deal at Roma last term and the Serie A club are keen on signing the England international on a permanent basis.
United had been seeking around £25million for the former Fulham defender before the pandemic hit but they altered their asking price to a figure of closer to £20m to reflect the financial climate.
However, Roma have failed to get remotely close to that figure, instead offering around £12m for Smalling.
With just a fortnight left before the transfer window closes, United are keen on offloading Smalling but they’d rather keep the defender than accept a paltry figure for the 30-year-old.
And Solskjaer has suggested as much by revealing that the club are unwilling to let Smalling go for the current figures being suggested by Roma.
‘At the moment, we’ve not had any bids up to the level that we want,’ said Solskjaer.
‘So that’s the situation.’
The club have made just one signing so far this summer, with Donny van de Beek arriving in a £40m deal from Ajax.
United want to sign a right winger and a left-back before the window closes, with Porto defender Alex Telles hopeful of completing a move to the club by the end of the week.