Debt-ridden Schalke will allow Neuer to move in the close season - probably to Bayern Munich who have already asked for a meeting to discuss signing the 25-year-old - so they can claim a transfer fee rather than let him leave for free.
Local media estimate he would cost 20 million euros to buy from Schalke, who have reached the Champions League semi-finals where they face Manchester United but have had a disappointing Bundesliga campaign and are in mid-table.
"I wanted to be honest and explain my decision," a tearful Neuer told reporters at a packed news conference in Gelsenkirchen while fighting back the tears. "I want to develop further and take a new big step in my career."
"I want to continue playing in the Champions League, at the highest level. As a person I want to take a step that will allow me to stand on my own two feet," said Schalke's talisman who will leave the club whose junior team he joined aged five.
"Where there is a will there is a way," he told German broadcaster ZDF. "I think we can do it and if Schalke do not get any transfer fee next year then they will act in such a way so as to get an agreement."
"We hope he will come this year and if not this year then he will come next year."
"Bayern have asked for a meeting but we said that at this moment this is not possible given the important matches we have coming up. But certainly there will be a meeting and there will be talks at some point," Heldt told reporters.
Neuer is considered one of the best keepers in Europe having helped Germany to a third-place finish at last year's World Cup and Schalke to the Champions League semis for the first time.
Neuer's likely departure will probably trigger a merry-go-round of Bundesliga goalkeeper transfers with Schalke almost certainly needing to find a credible replacement.
