Everton have reportedly identified Burnley's Jay Rodriguez as an ideal partner for striker Nikica Jelavic.
Jelavic has impressed since his move to Goodison Park from Rangers in January and The Sun reports that Moyes is currently weighing up a bid for Rodriguez to partner the Croatian.
The 22-year-old has netted 21 times in the Championship this season and Burnley are rumoured to value the forward at £8m.
The transfer fee may prove to be a stumbling block for cash-strapped Everton and Moyes may have to sell players before making a firm approach for Rodriguez.
Rodriguez only has a year remaining on his current deal at Turf Moor.