Markovic was withdrawn just 26 minutes into his country's 1-1 Euro 2016 qualifying draw with Armenia last Saturday.
Reports had suggested that the 20-year-old had suffered a muscular problem that could keep him out for up to three weeks.
Such a lay-off would have ruled Markovic out of Serbia's home fixture with Albania on Tuesday, as well as several Liverpool matches - including their UEFA Champions League meeting with Real Madrid next week.
However, the former Benfica man has declared himself fit for Tuesday's game in Belgrade.
Posting on his official Facebook page, Markovic wrote: "I'm ready for the match tomorrow! Injury is not as bad as it seemed at first sight."
The news is sure to come as a relief to Liverpool boss Brendan Rodgers, who has already seen players such as Daniel Sturridge, Joe Allen and Dejan Lovren suffer injuries while on international duty this season.
