M'bami is currently trying to impress new Pompey chief Paul Hart, and he featured against Havant & Waterlooville in a friendly on Tuesday.
The 26-year-old - who has nearly 30 caps for his country - is available on a free transfer after leaving French giants Marseille earlier this summer.
He was linked with a move to Turkey, but is now looking to seal a move to Fratton Park.
M'bami is not alone in trying to earn a move, as fellow French-based players Johan Audel and Fabrice Pancrate are also training with the club.
Forward Audel spent last season with Valenciennes, whilst Pancrate - who has already interested Burnley this summer - is currently with Paris St Germain.
Finally, and possible the most interesting name trying his luck with Pompey is midfielder Eugene Bopp.
The former Nottingham Forest player has spent the last three years playing in the lower leagues with Rotherham and Crewe.
But Hart knows Bopp well from their time together at the City Ground, and after he departed Crewe at the end of last season, he has now offered the 25-year-old an unlikely chance to earn a possible Premier League deal.
Bopp, though, did not do his chances any harm on Tuesday as he scored both goals in their friendly clash at Havant.