The Bundesliga leaders have reportedly identified Zaha as the man to replace Christian Pulisic at Signal Iduna Park, with the United States international joining Chelsea at the end of the 2018-19 season.
However, Hodgson says there has been no conversations between the two clubs and is confident Zaha – who signed a new five-year deal in August 2018 – will remain at Selhurst Park.
"We don't know [about] that," he told a media conference when quizzed about the rumours.
"There has been absolutely no dialogue whatsoever between Borussia Dortmund and Crystal Palace Football Club.
"If I am going to comment every time a club is linked with Wilf Zaha, I will be talking about it for a long time.
"Wilf signed a long-term contract with Crystal Palace. He's very much our player.
"I'd be very surprised if there were any clubs out there who wouldn't think he's very good, but that doesn't mean to say they are going to try and buy him."
Hodgson has regularly had to deal with transfer speculation surrounding Zaha, who has become an integral part of the side since his appointment as Eagles boss in September 2017.
Zaha was also keen to play down speculation of a move to China, saying he was “flattered” by the offer but remained fully focused on the Eagles.
The 26-year-old has struggled to replicate his previous form this campaign, scoring just three goals and adding a further two assists in the Premier League.
However, such is his influence on the side, Palace went over two years without winning a game when Zaha wasn’t in the team before their 1-0 victory over Leicester in December.
The south London club are currently 15th in the Premier League, five points clear of the relegation zone.