The Premier League club confirmed the Uruguayan, a recent transfer target for Arsenal, would stay behind "as a precaution following an injury in training yesterday".
Liverpool announced on their website: "He will undergo a scan on his foot later today."
Manager Brendan Rodgers will take a 21-man squad that includes captain Steven Gerrard but is also shorn of Daniel Agger, Martin Skrtel and Glen Johnson who have what the club describe as "knocks".
Liverpool's announcement may cause a fresh rush of speculation concerning Suarez's future, however their position is clear in explaining the striker's absence from the trip.
Suarez has made it clear to the Reds he wants to play in the Champions League and that has alerted Arsenal, who have made two failed bids, the last an offer of £40million and £1.
Arsenal believed such a proposal would trigger a sale clause in his contract but Liverpool are adamant that figure only requires them to inform the player of the offer and negotiate if they wish to sell.
Suarez made his second appearance at Anfield in three days on Monday, when the club held an open training session for about 5,000 selected fans.
Just like during his 30-minute cameo in Gerrard's testimonial against Olympiacos on Saturday, the striker was cheered at every opportunity during the hour or so the players were out on the pitch but was reluctant to acknowledge such support.
The injury Liverpool have now revealed he sustained may explain that attitude.
Liverpool have taken a firm stance regarding the former Ajax striker since rumours began over his future, making it clear that they do not want to sell him. Yet conjecture about his future refuses to go away, with legal action and Premier League arbitration reported to be possible routes his advisers are exploring.
Suarez is suspended for the first six games of the season as his 10-match ban for biting Chelsea's Branislav Ivanovic is carried over.