Ronald Koeman called Luis Suarez to tell him he was not needed at Barcelona, asking him to look for a new team.
Ajax wanted to bring the Uruguayan forward, 33, home, but Suarez is still at the top level and they cannot compete economically with more powerful sides, like Paris Saint-Germain.
Marc Overmars, Ajax's sporting director, said as much.
"The chance of Luis Suarez coming is quite small," he admitted. "We have had contact but we have that with a lot of players, it's normal to od that with former players (from your side)."
Suarez played four seasons at Ajax before moving to Liverpool, between 2007-11, playing 159 games, scoring 111 goals and giving 66 assists.