Unai Emery is claimed to be trying to get rid of the Germany international, after three seasons in which he has consistently failed to impress at the Emirates.
Mustafi, though, is reported to want to stay at the club, despite rumours linking him with a move to the Italian capital.
"That's news to me", father and representative Kujtim Mustafi told romanews.eu.
"There is nothing behind it, he had no contact with the Roma or any other Italian association."
With Roma having sold Greek defender Kostas Manolas to Serie A rivals Napoli in a €36 million (£32m/$41m) deal this summer, new manager Paulo Fonseca is short of a central defender so Mustafi’s availability will almost certainly have come up.
While he has provided Arsenal fans with some impressive performances, fans have derided him for high-profile mistakes and plenty have taken to social media to express their pleasure that the club are apparently ready to see him go.
However, with club captain Laurent Koscielny angling for the exit, Emery would likely need to replace Mustafi before the transfer deadline on August 8 or risk leaving himself short of numbers at the back.
Pepe’s likely arrival for around €80 million (£73.4m/€89.2m) would eclipse the fee paid for striker Pierre-Emerick Aubameyang in January 2018.
It would also mean that the club will have broken their transfer record for the third consecutive year after Alexandre Lacazette joined in the previous window.
Lacazette limped off early on in Arsenal’s most recent pre-season friendly against Lyon, but Emery has eased fans’ concerns about the severity of the blow.