The O’s are looking to strengthen their strikeforce for a tilt at League Two and have made the out-of-favour Town frontman a target, according to sources in London.
London-born Angol, who turns 25 at the beginning of August, is understood to be available to leave Montgomery Waters Meadow after failing to make an impact.
He spent the second part of his only season at Town on loan at League Two Lincoln but made just two substitute cameos.
Shrewsbury, who are still looking for another forward, signed Angol as a late replacement for the outgoing Stefan Payne last August.
The striker scored four times in 25 outings for Town but quickly found himself out of the team and down the pecking order.
Angol is one of several players that Sam Ricketts is prepared to listen to offers for as he trims his squad for the upcoming season.
Orient sold top scorer Macauley Bonne to Charlton earlier in the window for a reported £200,000.