His intervention comes as Lord Frost, the former Brexit negotiator now in charge of EU relations, heads to Brussels on Thursday evening amid ongoing efforts to resolve disagreements over the protocol between the two sides.
Lord Frost will have dinner with Maros Sefcovic, the European Commission vice president, following days of positive discussions over the timing and implementation of new checks and rules on goods crossing the Irish Sea as required by the protocol.
Both sides on Wednesday played down the expectations of a breakthrough, with UK sources stating that significant differences remained despite positive talks in recent days.
Lord Frost will also hold separate talks earlier in the day in London with Brandon Lewis, the Northern Ireland Secretary, and Irelands foreign minister Simon Coveney.
The Telegraph understands that Mr Lewis will urge Ireland and the EU to step up its engagements with unionists in Northern Ireland, having told MPs on Wednesday he believed there was a lack of understanding around the challenges the protocol posed for their sense of national identity.
However, while the UK and EU insist the protocol must remain in place, Mr Bassett said: I just do not think that tinkering with the protocol at this stage is going to do the trick.
He went on to state: “Arlene Foster was quite prepared at one stage to accept the border and the Irish say, but I don’t think she envisaged at the level at which it is at the moment.
“And I think the only way you’re going to stop this is for the Irish and British government and the parties in Northern Ireland to get together and hammer out a deal and hand it to Brussels.
“People in Brussels have been telling me that even the people who are in negotiations with Lord Frost say they have difficulty when they come back to Brussels with the ideologues who sort of say, well, this the Single Market, you know, as if, you know, a group of some English sausage going to Belfast, is going to undermine the Single Market.
“Even in Brussels, there are people who say they have difficulty getting even minor concessions too. I think we do need to take it out of the hands of the ideologues from Brussels and get down to practical application.”