Bernd Lange, who was heavily involved in Brexit negotiations and chairs a European parliament committee, said: "I would love to see the UK back." He said the EU missed the UK in decision-making because of its strong history of promoting open markets and democracy.
The comments revive a model that was rejected by the former prime minister Boris Johnson. A Swiss-style relationship with the EU involved free movement of people and regulatory alignment, which Johnson opposed, but it is often considered a halfway house to full membership of the bloc.
Switzerland is not a member of the EU, but last year it struck a deal cementing its "frictionless access" to the single market across more than 100 agreements under a new framework deal. That gives it access to the EU's electricity market, space programmes, Erasmus and the Digital Europe research programme, as well as participation in the European Centre for Disease Prevention and Control.
In exchange, Switzerland agreed to the free movement of people and to pay €375m (£326m) a year into the EU's economic and cohesion funds. Whether the UK would accept similar terms would be central to any such negotiation.