The UK government criticized Sheikh Mansour for meeting with the Syrian president.
He was pictured with the deputy prime minister.
The Foreign Office said such meetings undermine the prospect of peace in Syria.
Assad's trip marks a potential thaw in Syria's relations with its Arab neighbours, which had previously isolated the Syrian president.
The rulers of the United Arab Emirates indicated a willingness to strengthen ties with Syria.
In a statement to The Athletic, the Foreign, Commonwealth and Development Office (FCDO) responded to the move by saying: "It is the UK's firm belief that - in the absence of a change in behaviour by the Syrian regime - strengthening ties undermines the prospect of a lasting and inclusive peace in Syria."
Labour MP Chris Bryant, chair of the All-Party Parliamentary Group on Russia, shared those concerns and, in an interview with The Telegraph, went on to question if Mansour was a "fit and proper person to be owning a football club".
Manchester City has been contacted by the BBC.