Diouf, 21, joined West Ham United from Slavia Prague last summer in a £19 million deal and has developed into one of their most consistent performers despite the club's broader struggles near the foot of the table.
He has contributed five assists in 30 appearances across all competitions, with his crossing quality and defensive improvement across the second half of the season drawing admiring glances from across the Premier League.
The Guardian report United have identified Diouf as a primary left-back target, with at least one other leading Premier League club also monitoring the Senegalese international.
United's need is clear. Shaw, 30, has been reliable this season but carries a significant injury history, while Tyrell Malacia is set to depart on a free transfer and Patrick Dorgu is expected to operate further forward. Academy options Diego Leon and Harry Amass — both 19 — are not considered ready to challenge Shaw at senior level next season.
Midfield remains United's first transfer priority, with two signings in that area expected before attention turns to the left-back position. The pursuit of Diouf is expected to accelerate once the midfield business is concluded.
West Ham are aware of United's interest and have no desire to sell, but their precarious league position — 17th, two points above the relegation zone with four games remaining — may significantly limit their leverage in any negotiation.
Diouf has previously stated his ambition is to reach one of the five best clubs in the world, comments that will encourage United even if West Ham resist an opening approach.