Mr Lewis did say that he wanted to see a resolution to differences “as quickly as possible”.
Speaking during a visit to Co Down, he added: “I’m not setting arbitrary time frames.
“As I say, myself and the Foreign Secretary (Liz Truss) will be meeting with Maros Sefcovic on Thursday this week; there’s a series then of talks that will hopefully follow that building on the work we’ve already done.
“Our position hasn’t changed – we need to resolve this in a way that works for the people of Northern Ireland and we want to do that as quickly as possible.
“We want to do that in a way that is sustainable and can deliver for people.”
The Foreign Secretary was handed responsibility for the negotiations with the EU over the protocol after Lord Frost resigned as Brexit minister last month.
On Monday, Ms Truss held meetings with the DUP and Sinn Fein, after Sir Jeffrey indicated a “pause” on the DUP threat to collapse the powersharing institutions at Stormont over the protocol pending the outcome of renewed negotiations between the UK and EU over the Irish Sea trading barriers.
Sinn Fein deputy First Minister Michelle O’Neill said the Foreign Secretary told her that she did not want to trigger Article 16 of the protocol.
On Tuesday, Ms Truss held a virtual meeting with business representatives in Northern Ireland.
Roger Pollen, from the Federation of Small Businesses, struck an optimistic note after the meeting.
“In the meeting today I think there was a real sense amongst the business community and the politicians present that they know what needs to be done, there is a landing zone, there’s a reasonably good spirit and there’s an expectation that things can be achieved fairly quickly,” he told the BBC.
Retail NI chief executive Glyn Roberts said: “We outlined a number of difficulties many of our members are experiencing when trading with GB-based suppliers and wholesalers.
“This issue needs to be resolved as a matter of priority to ensure that consumers are given the full product range in Northern Ireland.
“We need a long-term sustainable deal which ensures stability, certainty and affordability for the broader business community in Northern Ireland.
“Business needs to be a partner in finding a broader agreement which keeps the benefits of the NI Protocol but fixes the problem of GB-NI trade.”
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