In conversation with Natasha Kaplinsky at the Board's President's dinner, he told the audience: "My position is fixed because of who I am."
Mr Blair said: "I think there will be a lot of people, people that I know who will want to vote in this election for people who stand up for what is right and what is good and what is positive about politics."
Asked if he would tactically vote himself he said: "I can't."
But in a sign that Mr Blair did not expect to see Mr Corbyn in Downing Street, he spoke of the forthcoming battle to regain the party from the far left.
He said: "Let me be frank, there is going to be a complete battle in the Labour Party because what has happened over these past years – particularly over antisemitism – is absolutely killing the party.
"There is going to be a big battle to pull the party away from all that politics."
Heaping praise on MPs such as Dame Margaret Hodge, Ruth Smeeth and Lord Mann, he said: "It is essential we have some people who are going to stay and fight this out."
He added: "There are really good Labour MPs that are standing in this election. People I know, people I've worked with.
"People who have stood up very strongly on antisemitism in the Labour Party and I want to see them supported."
Mr Blair singled out the "appalling" treatment suffered by Jewish MP Luciana Berger as she was forced out of Labour.
Pointedly, he told the MP, who was at the event, that he "wished her very well in her campaign" to win the Finchley and Golders Green seat in north London for the Liberal Democrat party.
"I think in this election there will be more people who look carefully in a non-tribal way – they will look carefully at the candidates in their constituency to a bigger degree than at any election I can remember," he added.
Mr Blair said that he believed the rise of left-wing antisemitism was "not limited to a few bad apples" and added it was a "phenomenon".
He spoke of the need to re-educate people "obsessed with a hatred of Israel" about the true meaning of Zionism.
He added: "I am having more reasonable conversations about Israel with some of the Arab states than I am back home with parts of the left."
Later, Home Secretary Priti Patel addressed the event, which was attended by MPs Mike Gapes, Mike Freer, Dame Louise Ellman, Dame Margaret Hodge, Lord Dubbs, Baroness Ludford and Lord Levy, amongst others.
The Home Secretary praised the Board for standing up for the Jewish community and said the current government was on their side.
Earlier, Board President Marie van der Zyl spoke and said it was "not acceptable or desirable" for there to be a stand-off between the Jewish community and the main opposition party in the UK.
Ms van der Zyl praised Mr Blair as a "true friend" of the Jewish community.
