The Hammers boss has not been hanging around in the transfer market, after already signing Argentine striker Mauro Zarate from Velez Sarsfield as well as highly-rated defender Chiekhou Kouyate from Belgium outfit Anderlecht.
France Under-20 star Kolodziejcza, 22, who previously played for Ligue one giants Lyon, is expected to arrived in east London later this week to agree personal terms and undergo a medical in what would be a reported four-year-deal with the club.
Allardyce has been intently searching for a left-back, after releasing George McCartney and deciding not to sign Columbian left-back Pablo Armero who had a somewhat disappointing six-month at Upton Park last summer.
This may come as a big surprise for many people, after Armero has produced a series of impressive displays at the World Cup, helping Colombia reach the quarter-finals.
Before any talks with the Ligue 1 club, there had also been rumours that West Ham were close to signing Argentine left-back Emanuel Insua from Boca Juniors, but they have now seemed to of faded away.
However, West Ham have been the only club to approach Nice and have not wasted much time in pursuing their target with negotiations now look to be in their final stages.
Big Sam, as he is affectionately known, would of been thanking his lucky stars last month, as West Ham owners David Gold and David Sullivan opted not to sack him, despite heavy criticism and even ugly protests from the fans last season.
Although, the Hammers chiefs clearly underlined their requirements for Allardyce, by demanding a dramatic improvement with the side and have offered a £20 million budget to do.
The key element being to change their long-ball style of play, which has been famously associated with the former Bolton, Newcastle and Blackburn manager.
The introduction of Kolodziejczak, along with his other two signing, will offer a refreshing options for West Ham as they ambitiously look to improve on last seasons disappointing 13th place finish and climb into the top 10. No pressure on Allardyce then.