Manchester United boss Mourinho wants Woodward to splash the cash with just four days of the transfer window to go.
The Red Devils signed Fred, Diogo Dalot and Lee Grant early on but, since then, they have failed to land several top targets.
Express Sport understands Manchester United will bid £80million for Harry Maguire, with Ivan Perisic, Willian and Toby Alderweireld also linked.
And Mourinho has now called on Woodward to deliver what he wants.
Speaking ahead of United’s pre-season clash with Bayern Munich, he said: “My CEO [Ed Woodward] has known what I want for quite a long time. He knows what I want.
“I know that he tries his best for me. I still have a few days to wait to see what is going to happen.”
Jose Mourinho also thinks that, with Liverpool and Manchester City strengthening, United may endure a tough campaign.
He added: “The other clubs that compete with us, they are really strong, or they already have fantastic teams and squads like Chelsea, Tottenham, Manchester City… or they are investing massively, like, for example, Liverpool, who are buying everything and everybody.
“So if we don’t make our team better it will be a difficult season for us.”
Mourinho wants two signings to turn United into Premier League champions.
But, last week, he suggested he would only end up with one new arrival.
The United boss said: “I am confident I will get one, but I think two I am not going to get – which is not a drama.
“In every pre-season it happens the same, with every club, which is that the manager wants more.
“It’s our nature, you always want more for your team, but then club decisions are different and normally you don’t get what you want, which happened during all my career.
“So, if I get one player until the end of the market, that’s fine.”
Who is Manchester United boss Jose Mourinho?
Age: 55
Country: Portugal
Honours: Primeira Liga (2003, 2004)
Taca de Portugal (2003)
Supertaca Candido de Oliveira (2003)
Champions League (2004, 2010)
UEFA Cup/Europa League (2003, 2017)
Premier League: (2005, 2006, 2015)
FA Cup: (2007)
EFL Cup: 2005, 2007, 2015, 2017)
Community Shield (2005, 2016)
Serie A (2009, 2010)
Coppa Italia (2010)
Supercoppa Italiana (2008)
La Liga (2012)
Copa del Rey (2011)
Supercopa de Espana (2012)