Dutch midfielder also being tracked by Serie A rivals AC Milan.
Roma have reportedly agreed terms with PSV midfielder Kevin Strootman, with speculation suggesting Daniele De Rossi is on his way out.
It is understood that the Giallorossi have agreed personal terms with the Dutch international, but are yet to agree to the club’s €15m valuation of the player.
According to La Gazzetta dello Sport, Roma have emerged as favourites to land the star, who has also been of interest to Premier League champions Manchester United and rivals AC Milan.
However, while PSV are requesting €15m plus performance-related bonuses, Roma are believed to want to reduce that figure to around €11m.
In contrast, speculation suggests that his arrival marks the end of the road for Daniele De Rossi, who is reportedly being tracked by Chelsea.
The 29-year-old has been a long-term target of Jose Mourinho, and given his troubles on and off the pitch in the Italian capital last season, it is unclear as to whether he will remain with his boyhood club.
Club president James Pallotta said last month that all the players at the club potentially had their price, which may see De Rossi sacrificed in order to strengthen the squad for new boss Rudi Garcia.
PSV had previously stated that Strootman would not be sold this summer, requesting that the player stay for another year before being allowed to move on in twelve months time.
However, it is looking more likely that the 23-year-old will become the second player to leave the Dutch giants for Italy this summer, with Dries Mertens sealing a €9.7m deal to Napoli last month.