According to the Guardian, Mr Whitty was reluctant to put his name to a public show of support for the policy this week.
Mr Johnson will unveil his roadmap out of lockdown on Monday and is expected to announce an across the board return for all year groups.
Initially a phased return to the classroom had been touted but the prime minister’s confidence is said to have been boosted by tumbling infection rates and a successful vaccine rollout.
However, some school leaders have expressed concerns about the ability to carry out regular Covid tests for secondary school pupils if all pupils go back at once.
Meanwhile young children aged five and 12 are now among the groups where Covid-19 is most prevalent, potentially heaping more pressure on primary schools.
The source told the Guardian Mr Whitty was at best “lukewarm” over the proposal and indicated negotiations behind the scenes were ongoing between cabinet members and scientists.
A government spokesperson said the claims made in the Guardian about a spat between the Prime Minister and Chief Medical Officer were “categorically untrue”.
They said: “We know schools, parents and pupils need clarity on plans as soon as possible, which is why we have committed to providing two weeks’ notice for them to prepare.
“The Prime Minister is due to set out plans for schools reopening on 22 February, and pupils will return from 8 March at the earliest.”
During the lockdown only vulnerable children and those of key workers have been permitted to attend school.