Kante has not trained with any of his EPL teammates since day one of the no-contact sessions, as the France international remains concerned about contracting coronavirus.
EPL giants Chelsea have given Kante their full backing over the situation, with reports claiming they are prepared for him to miss the remainder of this 2019-20 campaign.
Kante wants better health assurances after his brother died of a heart attack in 2018, just beforer the World Cup in Russia. Three months earlier, the EPL midfielder fainted in front of teammates after a training session - prompting fears over his health at the time.
According to a Telegraph report, Lampard is keen to 'fill Kante in on the science' behind the EPL's decision to move to phase two of training.
The 29-year-old has continued reporting for his COVID-19 testing in the meantime, so will be free to resume first-team training when he decides it is safe to do so.
Kante has been keeping fit at home with Lampard's blessing and the Blues are not willing to pressure him into making a return.
Lampard remains in constant contact with Kante and will feedback precisely what the latest move means, as well as new protocols, so the World Cup winner can decide whether or not to remain at home.
Experienced goalkeeper Willy Caballero, who signed a new extension earlier this month, revealed Kante was worried at one point that he had contracted the virus during lockdown.
"He tested negative for Covid-19 but had a bad time of it during quarantine with symptoms of the virus that gave him that fear. We respect him and we'll wait until he feels comfortable because the truth is that to do what we're doing you have to feel okay, feel confidence and after we start again, we have to all go forward together.
N'Golo is a very humble, hard-working person who is always smiling and must have his reasons to lift up his hand and say what he's said."
EPL set to resume in late June
The EPL is expected to resume the 2019-20 season at some point in late June and recently announced four more coronavirus cases from the latest round of testing.
Watford defender Adrian Mariappa and Bournemouth goalkeeper Aaron Ramsdale are among the EPL players who contracted the virus this month - both were asymptomatic.
The EPL have also increased the number of COVID-19 tests to 60 per club, as squads have now resumed contact training. This allows for managers to utilise Academy players in sessions that need higher numbers.
Chelsea are three points ahead of fifth-placed Manchester United in the EPL's final Champions League qualification spot, with nine games still to play.
They were also into the FA Cup quarter-finals, while having a mountain to climb (down 3-0 on aggregate) vs. Bundesliga champions Bayern in their UCL last-16 tie before the pandemic.