He is expected to share analysis of the health, economic and social ramifications of the measures taken to suppress the virus ahead of a crunch Commons vote on Tuesday.
Several Conservative MPs have threatened to rebel over the new tier system in England, which the Government wants to bring into force on Wednesday when the national lockdown ends.
Mr Johnson wrote a letter to his Conservative colleagues on Saturday evening, confirming that the new rules could end in nine weeks’ time.
Under his so-called “sunset” clause, the tiers would be lifted on February 3, with MPs offered a vote to extend them.
But despite offering MPs another chance to vote on the restrictions early next year, several said they still have reservations.
Conservative MP Peter Bone said he was “undecided” and would make his mind up after seeing the impact assessment, telling the PA news agency: “The dilemma I have is do we do more damage by the tiered system of lockdown, or do we do less.”
Another senior Tory backbencher said that his vote was “still in the balance” as he urged Mr Johnson to provide analysis of how the tier restrictions will affect businesses, saying he did not have confidence that the Government was really considering their needs.
Labour has not yet said whether it will support the tier system. If the party votes against it and if Mr Johnson suffers a major rebellion from his own MPs, the Government could lose the vote.
George Eustice told Sky News on Monday morning that he was aware up to 100 people have “got concerns” about the new coronavirus restrictions.
The Environment Secretary said: “The chief whip, obviously, will be talking to those MPs who have got concerns. I’ve seen suggestions that there could be up to 100 or so people that have got concerns.”
He added: “I think there is great frustration with the emergency measures that we have had to take to deal with this pandemic.
“We haven’t taken them lightly. We have had to take these to get the virus under control.
“What we need to show to those MPs and to the country at large is that we have got a clear route towards fixing this problem and turning the corner.”
When asked if the Government would have to rely on Labour to get the coronavirus restrictions through the Commons, Mr Eustice said: “It will depend on what other parties do.
“Yes, it will depend on what the Labour Party chose to do.”
Additional reporting by PA Media.