The 60-year-old senator has expressed his desire to buy a 35 per cent stake in the Premier League club to turn around the fortunes of the Gunners.
Enyeama was part of the Peoples' Elephant’s team during Kalu’s reign as governor and urged the politician and businessman to use his money to develop Enyimba rather than taking it abroad.
“Why not invest that money in Enyimba and turn it into a mega-club,” Enyeama tweeted.
“A club that will bring in a lot of sponsors and create job opportunities for the youth. Nigeria has no mega-club side that we can boast of.”
Kalu revealed his desire to invest in the Gunners is inspired by his quest to help the club win more trophies, including the Champions League and the Premier League.
“Our success with Enyimba FC between 2000-07 has continuously increased my passion for football," Kalu tweeted.
“As the pillar of sports in Africa, I am considering an investment in football and I will buy 35 per cent stake in Arsenal FC.
“Our target is to lift the Champions League and the Premier League, and valuable investment as well.
“Doing what you love and loving it is where greatness lies. I need 35 per cent of Arsenal to bring back trophies.”
Enyeama played for three years with Enyimba before leaving Nigeria to continue his development with Israeli Premier League club Bnei Yehuda.
The goalkeeper also featured for Hapoel Tel Aviv and French club Lille before his retirement from professional football.