The Daily Mail says the former Chelsea boss has asked Hajduk chairman Mate Peros for time to consider his next move after being presented with a package that would make him far and away the highest paid coach in Croatian football.
Grant wants two weeks to think it over, and Pini Zahavi is understood to have interpreted that as a sign of strong interest in a possible return to Fratton Park.
Zahavi is closing in on a takeover deal after being alerted to present owner Sacha Gaydamak's willingness to sell. Portsmouth have already held preliminary talks with potential new owners from South Africa, but Zahavi is believed to be further down the line to assuming command.
Should he succeed, it seems certain he would try to introduce a management structure that would include Grant, in his former role as director of football, and Croatia national coach Slaven Bilic as first-team boss.