The Portuguese front man is on Kenny Jackett’s radar this summer, according to Lincolnshire Live.
Andrade has impressed for the Imps as they lifted the League Two title this season, scoring 11 goals.
Aston Villa are also said to be following the 25-year-old's progress.
Andrade will be a familiar name to Pompey fans, after being linked with a move to Fratton Park in the past.
He spent a period on trial with the Blues last season, after catching the eye with Boreham Wood in the National League.
The former QPR man bagged 22 goals in the fifth tier, before moving to Sincil Bank in the summer.