The 21-year-old has agreed a loan deal with Rangers, according to the Scottish Sun.
Ojo spent last season with Stade Reims in Ligue 1 and the move to Ibrox will be his fifth temporary spell away from Anfield.
Rangers boss Gerrard earmarked the player as one of his key targets.
Yet, Ojo's signing won't mean the end of the club's interest in bringing Ryan Kent back to the club.
The Liverpool winger impressed in Scotland last season, winning the PFA Young Player of the Year.
He has had interest from both Aston Villa and Leeds United but it is believed that the former have pulled out of trying to recruit the 22-year-old.
Liverpool have put a £12million price tag on the player but Gerrard is hoping to do another loan deal.