The shift across the English Channel would see the former Highlanders star link up with his old mate Lima Sopoaga who is having a difficult first season at Wasps.
The Times reported on Wednesday (NZT) that an official announcement on Fekitoa's move was expected "in the next few days". It would be a welcomed signing for a proud Wasps club about to lose some significant talent in the form of England test No 8 Nathan Hughes, Springboks fullback Willie le Roux, highly regarded tighthead prop Jake Cooper-Woolley, and probably England outside back Elliot Daly.
The move to England would appear to wipe out any hopes Fekitoa had earlier expressed of returning to New Zealand to try to win back his All Blacks jersey in a crowded midfield department.
The 26-year-old Fekitoa surprised many with a sudden departure to France to join Toulon for the 2017-18 season after playing the last of his 24 tests for the All Blacks against the touring British & Irish Lions.
It was another case of an All Black lost too soon amid the growing trend of younger stars leaving New Zealand for offshore riches.
Fekitoa has been on a reported salary of around $700,000 at Toulon.
Toulon look set to continue their high turnover of talent as they endure a difficult season in the French Top 14 where they lie 11th in the Top 14 with five wins and nine losses.
But Fekitoa will find Wasps, so used to success in Britain and Europe, also going through a rough patch. They have six wins and six losses and lie sixth in a tight playoffs race.
Former Hurricanes and Wellington captain Brad Shields joined Wasps last year as he gained England test honours.
Fekitoa's presence would certainly be a welcomed boost for Sopoaga who has endured a fair bit of criticism for failing to transfer his dynamic New Zealand game to the English scene.
Fekitoa can play at second-five or centre putting him virtually on the shoulder of Sopoaga.