The phrase "rumoured interest" means there is a rumor or suggestion that someone is interested in something, but it has not been confirmed or proven yet. Full definition
Luis Suarez has declared his desire to stay at Liverpool amid rumoured interest from Manchester City (caughtoffside.com)
Despite rumoured interest in Chelsea's Petr Cech, it seems likely that Wojciech Szczesny will remain number one goalkeeper for now, but a major change could happen at centre - back with Winston Reid looking likely to leave West Ham United and attracting interest from both Arsenal and Liverpool. (caughtoffside.com)
Arsenal are reportedly asking for as little as # 35million for star defender Hector Bellerin amid rumoured interest from Spanish giants Real Madrid. (caughtoffside.com)