Saka has missed the Gunners' last two matches with the hamstring injury he sustained on international duty with England, while Timber has been absent for three games with a muscular problem.
Calafiori added to Arteta's woes when he suffered a knee injury in Arsenal's 1-0 Champions League win against Shakhtar Donetsk on Tuesday.
Captain Martin Odegaard remains out with an ankle problem and William Saliba will be suspended for the visit of Arne Slot's side after he was sent off against Bournemouth.
"We're going to do our very best to somehow have them (Saka, Calafiori and Timber) available, but it's very, very uncertain," said Arteta, 48 hours out from his side's fixture against the table-topping Reds on Sunday.
"Saka's done a bit of training on the grass. How far we can get him before Sunday is another question. We have another day, which is a good thing.
"Calafiori needs more tests. Yesterday he had some, and today he's going to have some more. After that we will know. Last time we thought it was really bad and then he ended up playing two days later. So let's see.
"And for Timber, this was the first session that he could have some involvement. He's been out for a while. We expected him to be further along than he is at the moment, so again we will have to see."
Arsenal's surprise 2-0 defeat at Bournemouth last weekend sees them trail Liverpool by four points ahead of the fixture at the Emirates.
Slot has enjoyed an impressive start to his tenure since he replaced Jurgen Klopp. Following their 1-0 win against RB Leipzig on Wednesday, they became the first Liverpool side to win their opening six away games of a season and the first to triumph in 11 of their first 12 matches.
A defeat for Arteta's men would see them fall seven points behind the Reds, and possibly out of the title race. But the defiant Spaniard added: "I never think about: 'What if we lose it?' Everything that we do is to win.
"In my preparation I don't spend one second thinking, 'if we lose it'. It's about 'if we win it', how convinced we are that we are going to win it and how we are going to feel afterwards.
"When we won against Aston Villa (in August) everybody was already saying 'if you lose this game, second game of the season, what's next?' We cannot think like this because we are only in October."
