The England international has spent the season on loan at Stadio Olimpico, making a total of 37 appearances in all competitions.
With the 30-year-old being out of favour at Old Trafford, Roma have been hopeful of negotiating a deal for the centre-back.
However, according to Sky Sport Italia, United are not prepared to budge on their £18m valuation of the player.
Having missed out on the Champions League, that has seemingly led to Roma informing the Premier League outfit that they will no longer be pursuing a transfer.
Smalling effectively has three years remaining on his contract at United.