Spurs and Inter are said to be in talks over a deal which would see Skriniar make the move to north London and Italian outlet Corriere dello Sport claim that Smalling is being lined up as a potential replacement.
Smalling impressed in Serie A last season, starring on loan at AS Roma and Paulo Fonseca's side are keen on bringing him back on a permanent basis.
However, Roma are yet to meet United's asking price and Inter could end up hijacking the deal.
The report claims that Fiorentina defender Nikola Milenkovic is Inter's top target to replace Skriniar but Fiorentina's demands have put them off.
As a result, Smalling has become the 'most likely option', with Inter able to use the funds they get from selling Skriniar to sign the former England international.
Red Devils boss Ole Gunnar Solskjaer was quizzed about the 30-year-old's future on Friday.
Speaking at a pre-match press conference ahead of United's trip to Brighton and Hove Albion in the Premier League, the Norwegian was asked if Smalling could stay at the club.
Solskjaer replied: "Different things need to happen then. Let’s see if there is that change. Let’s see what happens to Chris when the transfer window closes."
Get the latest transfer news straight into your inbox!
Want to be on the ball with all of the latest football news?
Well then sign up for the brilliant new Daily Star Sport email newsletter!
From the latest transfer news to the agenda-setting stories, get it all in your email inbox.
How do you sign up?
It only takes a matter of seconds.
Simply type your email address into the box at the top of this article and hit 'subscribe'.
And that's it, job done. You'll receive an email with all of the top news stories every single morning.
You can find out more information on our email newsletter on this link here.
It comes after Fonseca expressed confidence in his pursuit of Smalling earlier this month, saying: "I am confident Chris will return to Rome.
"We are working on Smalling. I am always in contact with him, even yesterday I spoke with him, he wants to come back and we want to have him back.
"I think that in the next few days we could have him back here with us."