Muntari had previously expressed reluctance to join Sunderland as he wanted a move to London, stating the capital was "the only possibility" at the start of the month.
But it appears his stance has now softened after discussions with Gyan and Mensah, and his agent claims the former Portsmouth midfielder could join the Wearsiders imminently.
"If everything is sorted out with Sunderland he will be going there," Fabien Piveteau told The Sun. "The other Ghana players at Sunderland - Asamoah Gyan and John Mensah - have told him about the club which has obviously played a part."
Muntari was a success at Portsmouth during the 2007-08 season, following a move from Udinese, and subsequently joined Inter for a fee of £12.7 million.
However, the 26-year-old has been restricted to only one Serie A start this season, and is frustrated at his lack of first-team football with the reigning Italian and European champions.