Mourinho, who was sacked in his second spell as Chelsea manager earlier this term, is widely considered to be the front-runner to replace van Gaal in the event of the Dutchman’s exit.
However, the Portuguese’s critics point to his off-field behaviour and reluctance to bring through youngsters as reasons why he shouldn’t get the job.
“Mourinho is very demanding and sometimes the players can’t take it,” Arnesen, who was sporting director at Stamford Bridge between 2005 and 2010, said.
“He made some drastic changes and it cost him. What would happen if they replaced van Gaal with Mourinho? The philosophy of Manchester United will go out of the window. But maybe they are that keen to have success.
“Van Gaal could not buy all his players, but he has done tremendously well with the young kids. Manchester United should give him at least one year more.”
Supporters have had to contend with van Gaal’s negative style of play for too long and it would be difficult to imagine the club sticking with him for another season.
Mourinho certainly has his flaws but he is the ‘safest bet’ in terms of getting United back to the top having won trophies at every club he has managed.