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The Manchester United boss has constantly been under pressure in his job, since taking it permanently in March 2019, but could take his side top of the table if they get at least a draw against Burnley on Tuesday night.
However, despite recent improvement, former Crystal Palace owner Simon Jordan believes that Solskjaer's job is far from safe and that Martial will eventually be the cause of his downfall.
The 25-year-old scored 23 goals last season but has only scored five times so far this season and has often been the cause of frustration.
Jordan has been one of Solskjaer's most vocal critics on talkSPORT and the businessman defended himself saying, "Man United fans are piling in on me, saying 'you've got this agenda against Ole Gunnar Solskjaer.
"It's not an agenda, it's calling out excellence and saying 'can you really subscribe to the fact that anytime soon this guy, and this group of players...' - because some of those players aren't fit for purpose.
"Anthony Martial will get you sacked if you have him regularly in your side because he's not good enough and he's lightweight.
"You look at this and say 'is he really going to bridge the gap in the cometh the hour, cometh the man moment against [Jurgen] Klopp and against [Pep] Guardiola?'
"He may well do it, he may well beat Klopp next week. I don't think he will but I don't take any satisfaction, I don't sit there wanting this man out of a job.
"I don't have an agenda, I'm just calling it as I see it. If you want to call it an agenda, that's peoples perspectives."
United's strikers have been a cause of concern for Solskjaer at times but at the end of last season he had Martial in form, as well as Marcus Rashford and Mason Greenwood on the wings scoring goals.
The trio scored 62 goals between them as United finished third in the Premier League and reached the Carabao Cup and Europa League semi-finals.
Solskjaer added Edinson Cavani to his squad in the summer and the Uruguayan has looked good when he's played, whilst it's believed that Erling Haaland has remained a high priority for the Norwegian manager.
:thumbsdown: "Part of the reason Man United aren't as aspirational is because of the manager."- talkSPORT (@talkSPORT) November 25, 2020
:white_check_mark: "Look at these managers and people want to sign for Guardiola or Klopp."@SJOpinion10 questions if #MUFC can attract top players with Ole Gunnar Solskjaer. :red_circle:
The Old Trafford side are currently level on points with defending champions Liverpool and could end the week six points clear of Jurgen Klopp's side.
Burnley is their game in hand of their rivals, after United started the season late due to the Europa League campaign ending late in August, and then they face Liverpool on Sunday at Anfield.
Solskjaer will need Martial, and everyone else, firing on all cylinders.
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