ESPNsoccernet has learned that David O'Leary and Glenn Hoddle are the big names to be linked to the managerial job at Portsmouth.
Hart is in danger of becoming the first Premier League managerial casualty of the season; hardly a surprise, given the fact that Pompey are pointless at the foot of the table.
However, the big shock is the big names on a potential list of replacements. ESPNsoccernet has been told that O'Leary and Hoddle would be the top two targets.
Both managers are not in employment with any club, so Pompey are not in breach of any rules should they decide to approach them. However, it would be a coup for Pompey and their new owners to land either of these big names.
And at this stage of the season, that would be more likely to cause less problems if Pompey's new owners went for managers not with rival clubs.
O'Leary and Hoddle fit the bill perfectly. O'Leary was wanted by Newcastle, but only rejected the move because of the uncertainties over the impending takeover.
O'Leary was one of the country's top managers at Leeds and took the club to a European Cup semi-final, and bossed Aston Villa between 2003 and 2006. He has been out of the game since being sacked by Villa.
Hoddle, the former England manager, has turned down 15 jobs since starting up his special academy in Spain. He turned down a top job offer in Holland only this week, and it would take something extraordinary to lure him away from his project.
Even before Pompey make an approach to Hoddle, should that occur, I believe the former Chelsea manager would turn them down as he has done so many other approaches.
Hart is inevitably under scrutiny after Portsmouth extended their dreadful season's beginning to a run of six successive defeats when they lost at Villa at the weekend, the worst start in Premier League history and the worst in the top flight since Leicester City in 1983.
Back then, Leicester had a young Gary Lineker, who scored 23 goals to help stave off relegation. Pompey saved themselves in the final fortnight of last season, but are now favourites to go down.