It is understood Rashford’s representatives have spoken to PSG about a switch to the Ligue 1 champions after a frustrating year at Old Trafford.
Rashford missed the start of last season with a shoulder injury before returning to score four goals in 25 Premier League appearances, losing his place in the England squad.
But Ten Hag insisted the 24-year-old, who has one year left on his contract with a club option for a further 12 months, remained integral at Old Trafford.
“He’s really important,” Ten Hag said. “You have seen from the first day I’m here, I’m really happy with him, I don’t want to lose him. He’s definitely in our plans at Manchester United.”
The speculation around Rashford comes as United continue to struggle to bring in signings of their own.
The club are no closer with their primary target, Barcelona’s Frenkie de Jong, while a report on Friday said the club’s board are blocking Ten Hag’s pursuit of Chelsea’s Hakim Ziyech.
A move for veteran forward Marko Arnautovic was aborted this week amid a fan backlash while the one player who does seem likely to join – France midfielder Adrien Rabiot – was criticised by former midfielder Lou Macari on Friday.
Speaking on in-house channel MUTV, Macari said: “I’d never really heard of him. Clubs spend millions of pounds scouting players across Europe, but nobody else has made a move for this fella. Why do you think this is? I have got a bad feeling about the guy.”
But, despite the mis-steps, Ten Hag insisted he and the club’s hierarchy are on the same page when it comes to transfer targets.
“I’m happy, I think we’re co-operating really well,” he said. “I cannot talk about players under contract at other clubs.”
Asked if he will have the squad he needs by the time the transfer window closes on September 1, Ten Hag added: “We have to. I am convinced we will have.”
The Portugal forward came on as a 53rd minute substitute as Ten Hag’s tenure got off to a losing start in last Sunday’s 2-1 home defeat to Brighton.
Ten Hag said Ronaldo would be involved at Brentford on Saturday, but would not be drawn on whether he will start.
“He had a good training week,” he said. “He’s had two half-games and for the starting XI we will see tomorrow. It’s my decision, I keep it.”
That could see Christian Eriksen again deployed in a false-nine role as he returns to face the club he left to join United in the summer.
There were boos at Old Trafford last weekend as many of the shortcomings that plagued United last season were still on display under new management.
The pressure will therefore be on at the Gtech Community Stadium but Ten Hag said he was ready for it.
“I know there is always pressure, I have the experience, how it is,” he said. “I know we have to win every game, I know the fans, I know everyone expects Manchester United to win every game.
“We have to deal with that and all I can do is prepare the team as well as I can this weekend.”