However, the Tynecastle side could find competition from across the city with the Steelmen boss a possible option for Hibs if Paul Heckingbottom was to be sacked.
According to the Scottish Sun, Robinson is on a shortlist of candidates drawn up by Hearts who currently sit bottom of the table after a 3-2 defeat to Motherwell at Tynecastle on Saturday.
The loss brought fan protests outside the Main Stand following the match with around 1,000 fans gathering to demand for Levein to be sacked.
There were chants during the game aimed at the man in the Hearts dugout.
However, Levein has maintained that he can and will turn it around.
Hearts go into Sunday’s derby without a league win since the end of March, while rivals Hibs are ninth with one league win from their last ten.
Robinson has impressed since taking over from Mark McGhee at Fir Park in 2017.
In the 17-18 season the Northern Irishman led Motherwell to two cup finals, while this season has built an attacking, young team.