Swift has kicked off the Championship campaign with eight goals and six assists in 14 appearances, drawing in supposed interest from Leeds and Newcastle as a result.
According to The72, Brentford have also identified the Englishman as a prime target for the January window and will rival the Premier League duo for his signature.
Such a move would be a return to the Bees for Swift, who joined Brentford on loan from Chelsea for the 2015-16 season, in which he netted seven goals and provided four assists in 28 appearances.
Since arriving at the Madejski Stadium in 2016, the 26-year-old has contributed 31 goals and 31 assists in 178 games for Reading, with the current campaign looking to be his most productive so far.
The Royals reportedly fended off interest in Swift from Sheffield United in the previous two seasons, but they are said to be battling with much more competition for his signature heading into January. body check tags ::