The Baggies attacking options are sparce, with Salomon Rondon the only recognised centre-forward currently being used by manager Tony Pulis.
Summer signings Nacer Chadli and Hal Robson-Kanu can also play there, although Saido Berahino continues to be overlooked as his contract wears down.
Hull boss Mike Phelan confirmed his interest in signing Rodriguez at Friday's pre-West Brom press conference, with the Baggies visiting the KCOM Stadium later this afternoon.
However, on current form a move to The Hawthorns is likely to appeal more to the Southampton striker, who has struggled for regular minutes since suffering a serious injury in May 2014.
However, it is claimed that the 19-year-old is not a priority target for the Baggies, as they seek players who can make an immediate impact at first team level.