Lallana, Markovic set to play against Olympiacos
Neither played a part as the Premier League side were beaten 1-0 by Roma in a friendly at Fenway Park on Wednesday.
Lallana and Markovic are two of the club's most expensive signings of the close-season and could feature against Olympiacos on Sunday.
Manager Brendan Rodgers said the duo, along with England internationals, are in line to play roles.
"They only really began training on Monday. I put Jordan Henderson in because of his level of fitness. Jordan could play 10 games on the spin because he's so fit and strong," Rodgers told a news conference.
"It was nice to give him a 15-minute period at the end. But those players, like young Markovic, who is an exceptional talent, will be involved when we arrive in Chicago."
Both Liverpool and Roma struggled to create many clear-cut chances in Boston before Marco Borriello's scrappy 90th-minute winner.
After losing two of three pre-season friendlies so far, Rodgers said results were unimportant – until his side's Premier League campaign starts against Southampton on August 17.
"It's not about results at this stage. The most important result for me is the first game of the season," he said.
"You have a choice - you can play friendlies that probably make you win every game and you might not find anything out. We've got a really tough set of fixtures over the course of the pre-season.
"We've got a great tour out here and then we go back and within a few days we'll play Borussia Dortmund. We're really pitching ourselves in at a good level to get a good gauge.
"The most important objective is that we're in a really good physical condition for our first game of the season, against Southampton.
"And that technically and tactically, we'll have honed up all of the principles and ideas that have made us so successful in the last couple of years. That will be the most important result for us."