The 23-year-old joined Bologna from Marseille last summer following a high-profile bust-up with former teammate Adrien Rabiot.
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Rowe scored eight goals and provided four assists in his 43 games across all competition for Bologna as they narrowly missed out on European football with an eighth-place finish.
According to Il Resto del Carlino, Chelsea have entered talks with Rowe’s representatives over a potential move to Stamford Bridge.
Chelsea are looking to sign a new left winger/forward this summer, with Garnacho expected to leave after just one season with the club.
Roma have been linked with a move for the Argentine, but Chelsea are unwilling to accept anything other than a permanent move.