Román has attracted attention for his performances at the base of Celta's midfield, earning comparisons with Spain international Rodri and the nickname “Mini Rodri” for his ability to control play from a deeper position.
The Sun suggests Fulham and Brighton have been monitoring the midfielder alongside Bournemouth, while Atlético Madrid are also said to be interested. No completed deal or formal offer has been confirmed.
Román has made an impression in LaLiga this season, reportedly starting six matches, scoring once and providing two assists before an injury interrupted his progress.
Celta Vigo confirmed in October that the midfielder had undergone surgery on his right knee after medical tests identified a loose body in the joint. The club estimated that his recovery would take between four and six weeks, provided there were no complications.
That absence could shape the timing of any potential move. A return during November would leave the 23-year-old with an opportunity to regain fitness before the January transfer window opens.
Román is a product of Celta's academy and has two years remaining on his contract, according to the reports linking him with a move. His deal is also reported to contain a release clause worth around £30 million.
For Fulham, a move would potentially add another option in central midfield as Álvaro Arbeloa continues to shape his squad. The club recruited several players from Spain during the summer, including three from Real Madrid, where Arbeloa previously worked.
Brighton are also understood to be keeping track of Román as they consider possible reinforcements. Atlético Madrid's reported interest could complicate matters for the Premier League clubs if the Spanish side decide to pursue a formal offer.
The comparison with Rodri reflects Román's role rather than an established equivalence in experience or achievement. He has developed as a controlling midfielder at Celta, but any move to the Premier League would represent a significant new stage in his career.
His immediate priority is recovery from the knee operation. With Celta expecting him to miss several weeks, his fitness and progress towards a return will be important factors in determining whether interest develops into a concrete transfer approach in January.