Media reports believe that Rangers will look to Hart as replacement for the now departed Jim Magilton who it was announced on Wednesday evening, had left Loftus Road by mutual consent.
Hart, who has also managed at Nottingham Forest, Barnsley, and Rushden & Diamonds, was relieved of his post at Pompey last month with the south-coast side struggling at the foot of the Premier League table.
Former Peterborough manager Daren Ferguson is another name being banded about in the press as possible successor to Magilton.