The Red Devils beat West Ham 3-0 in Sunday, their third win on the bounce.
It moved them to within six points of Tottenham in fifth, who occupy what is likely to be the final Champions League spot given to English sides this summer.
With Sir Jim Ratcliffe’s investment soon to be ratified, INEOS are keeping a close eye on Ten Hag.
And Keane feels the Dutchman is ‘on trial’ until the end of the season.
‘It’s a harsh word to use, “on trial”, because most managers are under pressure, but when you’re Manchester United manager, that pressure comes,’ Keane said.
‘Is he on trial? Yes, he probably is until the end of the season. If he doesn’t get his hands on the FA Cup or get into the Champions League, that pressure will be building.’
Gary Neville has been impressed with Ratcliffe’s work so far in appointing Omar Berrada from Manchester City.
A Sporting Director and head of recruitment are likely to follow, but Neville says Ten Hag’s position is the biggest call.
‘It’s the biggest decision for the new owners in the next few months,’ Neville said. ‘They’re going to bring a sporting director and a head of recruitment in, but whether they keep the manager is the one we’ll all be waiting on.’
For more stories like this, check our sport page.
Follow Metro Sport for the latest news on
Facebook, Twitter and Instagram.