Max Dowman walks out for Arsenal training alongside Declan Rice
Arsenal Football Newsletter
The Gunners drew the first leg of their last-16 tie 1-1 in Germany last week will look to secure a quarter-final spot in the return fixture in north London on Tuesday night.
They may have to do so without Odegaard, who continues to be sidelined by a knee injury.
The Arsenal captain has played just once since February 12, when he first picked up the issue against Brentford.
Odegaard briefly returned off the bench against Tottenham last month but had not fully recovered and has been absent since.
Timber, meanwhile, has been almost an ever-present in the Arsenal side this season but he is also now an injury doubt.
Timber attempted to carry on but signalled to the bench 20 minutes later and was brought off before half-time.
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Arsenal boss Mikel Arteta will provide an injury update on the pair at his pre-match press conference on Monday afternoon.
Leandro Trossard is pushing to be involved against Leverkusen after taking part in training.
The Belgian picked up a minor injury against Mansfield in the FA Cup last weekend that has kept him out of the last two matches.
Max Dowman was also involved in the first-team session on Monday morning.
The 16-year-old produced a remarkable cameo off the bench against Everton to drag Arsenal to victory.
Earlier this season, Dowman became the youngest player ever to feature in the Champions League and he could play a part in the second leg against Leverkusen.