The Colombian centre-forward has been a faithful servant to La Dea over the last four years, but with one year left on his contract, they want to cut ties with him this summer.
Roma have been linked with a move for several strikers in their search for a new marksman to lead the attack next season but to no avail.
They were reportedly closing in on a deal to sign Atletico Madrid striker Alvaro Morata, but the Spaniard has shut down speculation linking him with a move to Stadio Olimpico.
The Giallorossi have also been linked with a move for West Ham United misfit Gianluca Scamacca, but Atalanta have beaten them to his signature.
They have agreed a €32 million deal with the Hammers to bring the Italian back to his homeland just 12 months after leaving Sassuolo for East London.
The 24-year-old is set to replace Danish wonderkid Rasmus Hojlund, who completed a mega-money move to Manchester United over the weekend.
Muriel featured 31 times for Gasperini’s side last term, contributing three goals and five assists as Atalanta finished fifth in Serie A.
It remains to be seen whether Roma will jump at the chance to recruit Muriel, who has significant Serie A experience under his belt, having racked up over 300 appearances in the top flight.
Jose Mourinho has limited options in the striker department. With Tammy Abraham set for a lengthy spell on the sidelines, Andrea Belotti is the only out-and-out centre-forward in Roma’s squad.
The Italian arrived from Torino on a free transfer last summer but has failed to live up to expectations, notching just four goals in 46 outings across all competitions.
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