Mikel Arteta said in Monday's pre-game press conference that both men were 'close' to returning from their respective injuries, but he did not offer any guarantees on their fitness.
Timber has not played since sustaining a muscular problem against Paris Saint-Germain on October 1, while Saka picked up a hamstring injury during England's UEFA Nations League loss to Greece this month.
The latter was supposedly hopeful of being involved in the Premier League clash with Bournemouth at the weekend, but he ultimately failed to make the cut as Arsenal fell to a 2-0 defeat.
Saka's chances of being fit for the visit of Shakhtar appear slim too, as neither he nor Timber were spotted in the early part of the training session, which was opened up to the media.
Saka, Timber likely to miss Shakhtar game
As well as the English attacker and Dutch defender, captain Martin Odegaard was missing from the group too, although Arteta had already ruled the Norway international out of Tuesday's game.
Takehiro Tomiyasu, who has just suffered a fresh setback immediately after returning from a knee problem, was nowhere to be seen either, and hamstring victim Kieran Tierney is not expected to be involved on Tuesday.
However, William Saliba will be fine to play despite being sent off in the Bournemouth loss, as his suspension only applies to domestic games, but he will be absent for the crunch clash with Liverpool this weekend.
Second-choice goalkeeper Neto is also expected to be back in the squad after he was ineligible to face parent club Bournemouth at the weekend, as Arsenal chase a second win from three European games this season.
Arteta's men eased past Paris Saint-Germain 2-0 on October 1, two weeks on from their gritty goalless draw away to Europa League winners Atalanta BC, and the Gunners sit in 13th place in the League Phase table.
Could Saka absence lead to Ethan Nwaneri start?
With Saka sidelined at the weekend, Raheem Sterling began on the right wing at the Vitality Stadium, but the Chelsea loanee was the unfortunate player to be sacrificed for an extra defender when Saliba was given his marching orders.
Sterling will likely be given another chance on the right-hand side after being taken off through no fault of his own at the weekend, but 17-year-old protege Ethan Nwaneri is another option as he awaits his Champions League debut.
Arteta was asked in his pre-game press conference whether the English teenager could be seen from the first whistle on Tuesday, although he hinted that he would keep going with his cautious approach.
"I think it's identifying moments, understanding where he is, where the team is and what is the optimal moment to throw a player in that context," Arteta said. "He's already done a lot in a very short period of time. So let's take it step by step and make sure those steps are consistent and can allow him to grow in the manner and form that we want him in the team."
Arsenal have beaten Shakhtar Donetsk in both of their previous games at the Emirates, and their visitors are still waiting for their first win and goal of the tournament, drawing 0-0 with Bologna first up before a 3-0 loss to Atalanta last time out.