The 19-year-old Denmark international has been linked with a host of top European clubs after a breakthrough season last term and the player's agent claimed City had made a formal approach for the player.
Although City boss Roberto Mancini has confirmed he is interested in adding to the four summer signings he has already made, there is no offer in place for Eriksen.
A club spokesman said: "Manchester City strongly refute any suggestion that an offer has been made either to the player or his agent."
City have also privately rejected suggestions, originating in Italy on Saturday morning, that they have agreed to sign Manchester United target Wesley Sneijder from Inter Milan.
United are still thought to be interested in the Holland star, who is seen as a natural replacement to the retired Paul Scholes.
The classy Denmark playmaker is said to have been the subject of a "concrete proposal" from the Premier League club.
But the 19-year-old, who has been linked with several clubs around Europe, rejected a potential move to England in order to continue his development at Ajax.
"It is true that we have a concrete proposal from Manchester City, about which Eriksen is proud and honoured," Eriksen's representative, Martin Schoot, told Bold.dk.
"We talk about the world's richest club, so that they are interested is something Christian regards as an honour.
"But Christian said a polite, 'no thanks', because he did not feel it would be the best move for his career at this time.
"It also says a little about Christian as a person. It is clear that money does not mean the most to him.
But last season's FA Cup winners have no such agreement in place.
Source: Team Talk
Source: Team Talk