The England striker has been the subject of offers from West Ham and former club Newcastle and has not travelled with the Reds as they take on the Belarussian side on Thursday
The striker has picked up a groin injury and did not make the journey with the rest of the Reds team to face the side who finished third in Belarus' top division last season.
Carroll has been the subject of intense transfer talk this summer after new Anfield boss Brendan Rodgers admitted that he would be open to offers for the England international, who netted against Sweden at Euro 2012.
Newcastle, for whom the forward played before moving to Merseyside for 35 million pounds in January 2011, is interested in signing the Tyneside-born player and Goal.com revealed this week that the Magpies are preparing an £18m bid to bring the striker back to the Sports Direct Arena.
If Carroll were to feature in any of the Reds' Europa League qualifiers, he would still be eligible to take part in the Magpies' own campaign in Europe this term.
The 23-year-old has also interested West Ham, who were thought to have agreed a 2m pounds loan deal to secure Carroll, but have abandoned its interest with the striker not keen on a move to east London.