Alonso will undergo surgery on Thursday after breaking his ankle in Saturday's 1-0 defeat by Chelsea and Kirkland will have a back operation on Friday, Liverpool's official website reported on Wednesday.
Liverpool manager Rafael Benitez had been hoping Alonso would only be sidelined for six weeks but a specialist said on Tuesday the 23-year-old Spanish international would need a screw inserted into his left ankle.
Kirkland, whose career has been blighted by a number of serious injuries, is to have keyhole surgery on a disc in his lower back.
Their absence will be a significant blow for Benitez, whose team have improved to fifth in the Premier League with four wins in their last five matches.
