Carroll joined from Newcastle for £35 million in January following Fernando Torres' move to Chelsea, and has scored just two league goals for Kenny Dalglish's side since then - although his appearances have been limited by injury.
Meanwhile, England international midfielder Henderson cost a reported £20 million from Sunderland this summer, a fee that raised a few eyebrows given the amount of options available to Dalglish in central areas.
Given the Reds' significant outlay - Alexander Doni, Stewart Downing, Charlie Adam and Jose Enrique have also arrived in recent months - the pressure is on Dalglish to deliver a top-four place, a quest that was boosted by an impressive 2-0 victory over Arsenal on Saturday.
And Dalglish has told his doubters to pass judgement on the summer splurge later in the season. "If you want to buy [Carroll or Henderson] now, you'll pay more than I did," Dalglish said. "Bold? Stupid? Time will tell."