The Saints had no updates on Friday afternoon after the morning's session at Moorabbin.
King has another knee problem, while Sinclair hurt his hamstring and Wood is nursing a sore quad.
Given last week's bad injury news, with young gun Mattae Phillipou leading the casualties, the Saints can ill-afford a serious toll.
"We'll provide further information once we have those results," Saints football boss David Misson said in a club statement."We understand the interest in Max, Mason and Jack, but until we have the scan results, we're working in hypotheticals which is irresponsible."
Last week, the Saints announced Phillipou would miss the start of the season with a leg stress fracture.
Defender Dougal Howard also is sidelined with a dislocated shoulder and Rowan Marshall is managing a back injury.
King re-signed with the Saints last October until 2032, following a season where the key forward was restricted to only 12 games because of a knee injury.
King, when fit the centre piece of St Kilda's attack, had also been sidelined in previous seasons with shoulder injuries.
Taken at No.4 in the 2018 draft, King missed the '19 season as he recovered from a knee reconstruction.
He made his AFL debut in 2020 and has played 83 games, kicking 159 goals.
King showed just how good he can be when uninjured in 2022, playing 22 games and kicking 52 goals. But he has only managed 23 games over the last two seasons.
Sinclair finished runner-up to Callum Wilkie in last year's club best-and-fairest voting. The defender had won the award in the previous two seasons and is also a two-time All-Australian.
Wood played 18 senior games last season and found his niche on a wing.
Liam Henry, Paddy Dow and Hunter Clark are also injured as the Saints build to their round-one match on March 16 against Adelaide.
The Saints most recently made the finals in 2020.
Last season under coach Ross Lyon they struggled to 12th, two games outside the top eight with an 11-12 record, although the year ended on a high with wins over finalists Geelong and Carlton.