Labour has been in talks with the Jewish Museum over Jeremy Corbyn using the venue to address the growing anti-Semitism crisis.
Chief executive Abigail Morris said the situation was “delicate” and she did not want to agree to something that “will make things worse”.
Anti-Semitism campaigners said they would not be satisfied by “hollow promises delivered under duress”.
Ms Morris told The Jewish Chronicle: “We are still trying to work out what (Mr Corbyn’s office) is asking from us, whether it is a discussion, a statement or a speech.
“Things are very delicate at the moment.
“But the Jewish Museum is all about building bridges, and sometimes that’s hard.
“We would want to be part of a healing process, not something that will make things worse.
“We are very proud of being a cross-communal space and we want to be a place where positive dialogue can take place.”
Labour denied that the Labour leader was comparing the actions of Israelis to Nazis when he referred to the sieges of Leningrad and Stalingrad during a rally speech on Gaza.
On Wednesday, Mr Corbyn apologised for sharing a platform with people who reportedly compared Israel to the Nazis.
Shadow chancellor John McDonnell faced questions over his backing of the creation of an anti-Zionist group International Jewish Anti-Zionist Network (IJAN), which he supported in a 2008 Commons motion.
The Labour leadership’s reticence in adopting the International Holocaust Remembrance Alliance (IHRA) definition and its examples has become a flashpoint in the row over anti-Semitism in the party.
Gideon Falter, chairman of Campaign Against Antisemitism, said: “There has been speculation that Jeremy Corbyn wishes to address the Jewish community.
“Some have suggested that he intends to adopt the International Definition of anti-Semitism.
“Under that definition, he is an anti-Semite, as the revelations this week have shown us.
“We have seen this act before, and we are insulted that he thinks we will be satisfied by hollow promises delivered under duress.
“No matter what action Mr Corbyn promises, his track record demonstrates that he is an anti-Semite and an existential threat to British Jews.”