Riquelme, a renewable energy entrepreneur challenging incumbent Florentino Perez, made the pledge during an appearance on Spanish television on Wednesday, where he held up a Real Madrid shirt bearing Haaland's name.
"The stories which have emerged from Spain regarding the future of Erling Haaland are untrue," a City spokesperson said on Thursday.
"There is no chance of this happening and there is no contractual clause to enable it. We are considering legal action for the use of our player's image in this context."
Riquelme said Haaland, who scored 38 goals in all competitions last season, had a release clause and wanted to move to the Spanish club, adding that he would make the transfer a priority if he wins Sunday's election.
A joint statement from Haaland's father, Alfie, and the 25-year-old player's agent, Rafaela Pimenta, swiftly rejected the suggestion, describing it as "not true".
Riquelme added he would try to sign City's Spain midfielder Rodri, saying he had spoken to the player's agent and would "do everything possible" to bring the Ballon d'Or winner to Madrid.
The remarks come against the backdrop of Real's presidential election, the first in two decades in which Perez is not running unopposed, after the club's two seasons without a major trophy.
Voting is scheduled for Sunday, with around 100,000 club members eligible to take part.
Haaland had the option to join Real in 2022 when he left Borussia Dortmund but chose City, where his father played.
While the striker, who won the Premier League Golden Boot for the third time in four seasons, said he would like to play for Real one day, there has been no suggestion he is unhappy at City. He signed a new 9-½-year contract in January 2025.