The Manchester City man is currently on loan at Aston Villa, with the Mirror saying both clubs have agreed a fee ahead of a permanent move.
But West Brom think they have hope of luring Sinclair, who has played for them on loan before, to the Baggies.
Tony Pulis is said to see hope in the pursuit due to Jack Grealish keeping the 26-year-old out of the Aston Villa side at present.
The basis for West Brom's interest is reportedly Pulis's desire to recruit pacy players out wide. The policy sounds consistent with the Midlands club's other reported targets, with the Daily Mirror also previously linking them with a move for Queens Park Rangers winger Matt Phillips.
Should the Baggies' Sinclair interest prove concrete, it will be interesting to see which club he ends up choosing.
The ball should be in Aston Villa's court based on current standings but, if the winger does see himself as more of a starter at West Brom, he may well find the move one worth considering.