Smalling has been on loan to Roma this season and has already expressed hope of staying in the Italian capital beyond the terms of his agreement.
However, the more the defender impressed in Serie A, the more his price went up, United now demanding around £ 20-25 million for his permanent transfer.
The Roma do not have this type of cash available for free and are now considering other options.
In addition, Smalling had some concerns about the growing Covid-19 crisis in Italy, the nation being one of the most affected by the coronavirus.
Sport Witness reports that the 30-year-old has instructed his agent to seek out Premier League parties, with Arsenal among the clubs discussed.
Smalling is still hoping to win an England national team recall, and his best chance at doing so would be to play in the Premier League again.
If Smalling completes his return to England, it could open the door for Lovren to move on to the Stadio Olimpico, according to Corriere dello Sport.
The Croatian international has made only nine appearances for Liverpool this season and is now the fourth choice in the hierarchy of central defenders at Anfield.
At 30, Lovren realizes that he may have only one big contract left in his career and is desperate for first team football.
He has been linked to a move to Roma in the past and would like the opportunity to restart his career in a similar way to how Smalling changed his game.
Former Roma sports director Franco Baldini also reportedly recommended Lovren to club leaders.
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Liverpool would likely demand less than United for Smalling, as Lovren’s contract will expire at the end of next season.
There may even be potential for a double transfer involving Xherdan Shaqiri.
The Swiss midfielder is expected to leave Liverpool this summer and Roma strongly admire his talents.
Liverpool have reportedly set an asking price of around £ 16-18 million for Shaqiri, while Lovren is valued at around £ 15 million.