The striker, 34, is at United's Carrington training ground and is reportedly set to sign a one-year contract at the club.
He is a free agent following his departure from Paris St Germain at the end of last season, and will become new manager Jose Mourinho's second signing after the arrival of £30million defender Eric Bailly.
Ibrahimovic announced his retirement from international duty following Sweden's disappointing performance at Euro 2016
There had already been extensive speculation about his anticipated move to Old Trafford, and on Thursday he wrote on Instagram: "Time to let the world know
My next destination is @manchesterunited."
United also appear close to concluding the transfer of Henrikh Mkhitaryan from Borussia Dortmund
An agreement for the midfielder is yet to be formally announced but United's official online shop was carrying images of their new blue away kit, available to order with Mkhitaryan's name
The page was soon removed and an error messaged replaced it.
Source : PA
Source: PA