The Egyptian international striker joined Wigan on loan from Zamalek last season, and he sprang to prominence with 11 goals before the end of 2008.
His form saw him linked with a big money January move, with Aston Villa, Liverpool and even Real Madrid all said to be keen.
But Wigan stood firm and insisted they had first refusal, but after January Zaki's form dipped and he fell out of favour with manager Steve Bruce after he returned late from World Cup duty.
Now a number of clubs are said to be looking at a deal for Zaki, who is desperate to make amends for how his spell at Wigan came to an end.
"I know that my behaviour when returning late from international duty was unacceptable and I am truly sorry for that, this was my first time outside of Egypt and I made some mistakes," Zaki told skysports.com.
"I have learnt from those mistakes and they will not happen again.
"I want to thank Steve Bruce and Wigan chairman Mr [Dave] Whelan for the chance they gave me at Wigan and I want them to publicly know that I am sorry for the ways things turned out there.
"I want to return to England, to the Premier League, I know that I can score goals and I know that I will be successful for any team that takes me.
"I can promise any manager looking for a striker that I will score goals, that I will work hard and that I will give 100 per cent for the club, the fans, the manager and my team-mates.
"Everybody deserves a second chance and I aim to take mine. I understand that there are many clubs looking for a striker and the option to take me on loan from Zamalek is possible again this season.
"I have everything to prove and I know that I am good enough and now mentally strong enough to cope with the Premier League, I just need the chance to prove it."
Portsmouth have a long-standing interest in the player and they are still keen, but the likes of Wolves, Burnley, Hull, Blackburn and Stoke have all been linked with the player.