According to La Tribune de Genève, his lawyer has requested 250 francs per day for the 89 days he was held in the cell, to compensate for ‘moral wrong'.
Switzerland's highest court already sided with the former prisoner in a 2014 judgement that criticized the conditions in which he and another prisoner were held.
However the compensation was never paid, after Geneva's government dragged its feet over a technicality that was initially upheld by a court of first instance, said the paper.
But in February an appeal court threw out that judgement, saying the former prisoner was entitled to compensation. It ordered both parties back to the court of first instance to agree a sum.
The man's lawyer welcomed the decision, saying the case “will have consequences on other ongoing cases”.
The man's victim was at trial awarded a sum of 3,000 francs in compensation for the attempt on her life, notes the paper.
The Champ-Dollon prison has long been criticized for poor conditions sparked by over-crowding.
In 2015 a report by Amnesty International drew attention to the problems created by a prison that was designed for 376 prisoners but at the time housed 811.
That followed a 2013 walk-out by prison guards protesting against the high number of detainees and its impact on working conditions.
Switzerland's supreme court has several times ruled in favour of Champ-Dollon prisoners who brought complaints.
In 2014 a convicted cocaine trafficker had his sentence reduced by six months, said the Tribune, and last year the complaint of another drug trafficker was upheld by the supreme court which found that the conditions in which he was held infringed the European Convention on Human Rights.
To tackle the problem of overcrowding, the canton of Geneva plans to build a new prison named Dardelles. Work should start on the 227 million franc building in autumn 2018, with a projected opening in 2021, 24 Heures reported in November.
In Champ-Dollon there are on average 580 prisoners for 390 places, it said.