The Reds are believed to have made a £12.7 million offer for the striker as director of football Damien Comolli flew to Amsterdam on Monday hoping to meet with the player.
But the Dutch club have rejected the offer and advised they do not want to sell the 23-year-old at that low a price.
"We'll have to wait for them to come back with something more respectful," an Ajax spokesman told BBC Sport.
"We want to keep him - at least until the end of the season and preferably for the rest of his contract."
Ajax have recommended Liverpool’s next offer be much higher for the striker who has scored 81 goals in 108 appearances for the club and 16 goals in 38 games for his country.
The club spokesman added: "If you compare the €15m [£12.7m] Liverpool want to pay for Suarez with other transfers you can imagine that it's far too low for us.
"Luis is our top goalscorer for the last three years and also the man with by far the most assists as well.
"He was one of the big guys for Uruguay in helping them come third in the World Cup in the summer and he still has a contract with us for two-and-a-half years."