The 25-year-old Senegalese player jetted in to hold talks and undergo a medical after the two clubs agreed a fee on Wednesday.
If the deal is completed, Gueye will become manager Tim Sherwood's third summer signing following the arrivals of Micah Richards and Scott Sinclair from Manchester City, and Villa's biggest outlay on a player since they signed striker Darren Bent from Sunderland for an initial £18million in January 2011.
Gueye has made more than 130 appearances for Lille and helped the club to eighth place in Ligue 1 last season.
Source : PA
Source: PA