Davis has an overactive thyroid, but the club is confident he will overcome the setback.
“He’s got an illness and we’re addressing the situation, so we’ll be taking a conservative approach with him,” General manager of football Chris Connolly said.
“He’s a long-term player for us and we won’t be taking any risks.”
Davis’ illness is understood to be similar to what Bulldogs Shaun Higgins and Will Minson suffered last year.
In other injury news at Melbourne, Tom Scully (knee), Colin Garland (calf) and Max Gawn (knee) will face fitness tests in the lead-up to this weekend.
But midfielder Jordie McKenzie will miss one to two weeks with a groin injury and will not play against the Brisbane Lions at Visy Park this Saturday.
Big man Jack Fitzpatrick (foot) will also be sidelined for three to five weeks.
All-Australian James Frawley (shoulder) and second-year rookie Michael Newton (hand) are racing to be fit for the start of the premiership season.
The versatile Cale Morton is still five to six weeks away from resuming from a hand injury.
Ruckman Robert Campbell is out for another six to eight weeks with an achilles problem.
Fitzpatrick (foot) - 3-5 weeks
Garland (calf) - test
Gawn (knee) - test
McKenzie (groin) - 1-2 weeks
Newton (hand) - 4 weeks
Scully (knee) - Test