The Edinburgh club want to reinforce their attack after selling Esmael Goncalves and Jamie Walker and releasing Cole Stockton. Haber is available for a small fee but Hearts are also pursuing other options.
Tynecastle officials are concerned they could lose Kyle Lafferty if a good offer arrives and have drawn up a list of potential replacements as a contingency plan. Haber could be brought in even if Lafferty stays, although any move may also depend on Dundee being able to source another forward at short notice.
Haber, a Canadian internationalist, is 29 and has plenty experience of British football having also played with St Johnstone, West Bromwich Albion, Notts County, Crewe Alexandra, Exeter and Stevenage.
Hearts were this morning awaiting news from Switzerland on whether FC Sion will agree to loan out their Angolan midfielder Joaquim Adao. All three parties are in talks and Adao is keen to come to Scotland after falling out of favour at Sion.
The Swiss club have received a comprehensive financial proposal for a loan fee and Adao’s wages and were due to inform Hearts today whether they will agree to the deal or not.
Adao has already visited Edinburgh and been shown round Tynecastle and Riccarton. He is now back in Sion awaiting news on his future.