Mourinho has been left frustrated by the club’s inability to land his top targets over the summer.
And now the Manchester United boss has taken another jibe at Woodward by hailing the way Juventus do their business.
It comes after Mourinho met the Italian club’s owner Andrea Agnelli in the tunnel at Old Trafford before United’s 1-0 Champions League loss in midweek.
Mourinho said: “Before the game I told Mr Agnelli, ‘Since I left Inter, you have seven (title wins) in a row and it looks like the eighth is coming’.
“He told me, ‘I don’t want the eighth, I want ten in a row’ — and I think that’s a fantastic answer and a fantastic statement.
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“They won seven in a row, but they bought Cristiano (Ronaldo) and (Leonardo) Bonucci and Emre) Can and (Joao) Cancelo, so they always want more and more and more.
“I think the objective of the club is happiness related to football results and they are going to chase a treble. If it is not this year, they are going to chase it next year.
“If it is not next year, they are going to chase it in other years.
“I’m not going to discuss their structure. To be honest I don’t even know Juventus’ structure, but I like the criteria.”
The comments are unlikely to go down well with Woodward. Express Sport understand United have got a two-man wishlist as they look at potential replacements for under fire boss Mourinho.
United would like former Chelsea boss Antonio Conte – or Juventus coach Max Allegri – to take over the Old Trafford hot seat.
But they have competition for Conte as Real Madrid and AC Milan could both be looking for a new head coach this week.
Julen Lopetegui faces the axe at Real if they lose the El Clasico game to Barcelona this evening and Conte is now free after leaving Chelsea in the summer.
He impressed in his first season at Stamford Bridge winning the Premier League but it all came apart after he fell out with the Chelsea board over transfers.
Mourinho has won himself some breathing space after a recent turnaround in fortunes but it’s likely that United will call time on his stay at the club in the summer.