Turkish club Fenerbache were unable to finalise a move for Gyan last week and Rennes would need a large offer to let the 24-year-old leave this summer.
Bruce has already brought in several players in the current transfer window, including a loan deal for Manchester United striker Danny Welbeck and moves for Nedum Onuoha, Titus Bramble, John Mensah and Cristian Riveros.
However, Bruce does not see Welbeck as Jones’ replacement up front and is keen to bring in a star striker to fill the void.