Mr Verhofstadt, the European Parliament's Brexit coordinator, said such an outcome will depend on Britain's willingness to comply with standards followed by member states.
"I think both sides have an interest to be very ambitious. But how far this will go is very difficult to say because it will depend on what the willingness is of the UK side to also comply with a number of standards in the European Union," he told BBC Radio 4 Today.
"We are always saying 'No tariffs? OK. No quotas? OK.'
"But also - no dumping. That can be state aid, that can be ecological standards, social standards."
Frank discussion with @SteveBarclay. I presented the @Europarl_EN's resolution on citizen's rights, adopted this week by a large majority. A few adjustments from the UK & more action from some EU countries would end the anxieties of many UK & EU-citizens who deserve certainty. pic.twitter.com/IM5OtY9S5tâ€” Guy Verhofstadt (@guyverhofstadt)January 16, 2020
Asked on the outcomes if Britain does not sign up to such stipulations, he said: "It will be very difficult to have a broad free trade agreement at that moment."
He spoke with Stephen Barclay on Thursday and stated the Brexit secretary had conceded over allowing EU citizens to have a hard copy of their settled status confirmation.
Those who had settled status were previously told to use a screenshot of their confirmation on their phones as proof.
Mr Verhofstadt told BBC Radio 4's Today programme: "They said we are going to look at it so people can print it so they have a physical document.
"People will have the opportunity to have a printout, probably a PDF document.
"That was the conclusion of our conversation."
Boris Johnson has vowed to secure a free trade deal by the end of 2020, when the Brexit transition period following January 31 is set to run out.
This marks another blow for that, with the EU having repeatedly said it thinks the timeframe is too small to attain such an agreement.
Asked about chances of securing a comprehensive deal, which the EU has suggested looks unlikely be the end of December, the PM told BBC Breakfast: "Enormously likely, epically likely."
Pressed on the possibility of such an agreement not coming to fruition, he added: "You always have to budget for a complete lack of common sense."
The PM previously met with European Commission president Ursula von der Leyen to discuss the potential future deal, and she expressed her concerns that the transition period was too short to secure one.