Jeremy Corbyn has kept the door open for long-term UK membership of the EU single market after Brexit.
And the Labour leader said he wanted Britain to retain membership of "many" EU agencies following its withdrawal from the 28-nation bloc.
Mr Corbyn also said he hoped the UK would "forever" remain a signatory to the European Convention on Human Rights and subject to the European Court of Human Rights, which is not an EU body.
Labour announced last month it favoured continued membership of the single market and customs union during a transition period lasting as long as four years after the formal Brexit date of March 2019.
But the party is yet to announce a firm policy for the longer term, with shadow Brexit secretary Sir Keir Starmer saying Labour was "flexible" on the issue.
Asked about Labour's plans following the implementation period, Mr Corbyn told BBC Radio 4's World at One that he wanted the UK to continue to "trade within the single market" and said it was "open for discussion" whether this should involve formal membership.
"We want a relationship which allows us to trade within the single market," said the Labour leader.
"Whether that's formal membership - which is only possible, I believe, if you are actually a member of the EU - or whether it's an agreed trading relationship, is open for discussion."
Mr Corbyn has ordered his MPs to vote against the Government's EU (Withdrawal) Bill at second reading in the House of Commons late on Monday.
But he insisted he respects the result of the 2016 referendum to take Britain out of the EU.
"There was a referendum and I think we have to respect the result of the referendum," he said.
Nonetheless, he argued that Britain should not break off its close contact with EU institutions which enable cross-border co-operation on a wide range of issues.
"I want to build a relationship with Europe and I want to work in Europe - a Europe that works for the many, not for the few - and remain a member of European institutions," he said.
"We are obviously going to be forever signed up, I hope, to the European Court of Human Rights and the European Convention on Human Rights.
"But there are many other EU-related agencies that we should be members of and ensure that this close relationship of manufacturing industry and universities remains and the close relationship of peoples across Europe remains."
Mr Corbyn said he did not believe it would be possible for the UK to reach a new trade deal with the EU by March 2019, but declined to put a timeframe on the transition period, saying only it should last "for as long as necessary and as short as possible".
"The Leave date is set as March 2019," the Labour leader told World at One. "I don't see how it is possible to reach agreement on all the trade issues which are so necessary between now and then."
He warned of a "very damaging effect to a huge amount of industries in this country, manufacturing as well as financial services" if the UK is allowed to crash out of the EU without a deal in 2019 and forced to fall back on World Trade Organisation rules and tariffs.