The Edinburgh club are negotiating a proposal worth £175,000 for the 25-year-old energetic No.10, whose contract in Ireland has another year to run.
He is seen as a potential replacement for Olly Lee in the Hearts midfield and talks are ongoing ahead of tonight’s transfer deadline.
McEneff is highly rated in Ireland and has a number of suitors in England. However, Hearts have made their move to bring him to Edinburgh.
The player was previously on Tottenham Hotspur’s books before a spell with Derry City. He has excelled since joining Shamrock in 2018 and was called into the Republic of Ireland senior squad for the first time last November.
McEneff also has European experience, most notably last autumn when Rovers came up against Italian giants AC Milan in the Europa League.
Hearts hope to add him to their squad after completing the loan capture of Coventry City winger Gervane Kastaneer.