Brendan Rodgers was linked with several midfielders over the summer - including Chelsea's Willian and Henrikh Mkhitaryan - and the Anfield boss is expected to be busy again in January.
Rakitic, who is under contract until the summer of 2015, was mentioned as a January transfer target for Manchester United and Chelsea earlier this week.
But Le 10 Sport claims Liverpool are also keen on the Croatian international. Formerly of FC Basel and Schalke, the 25-year-old midfielder is a key part of the Sevilla set-up.
But following the summer departures of key players - Jesus Navas and Alvaro Negredo left for Manchester City and Geoffrey Kondogbia for Monaco - the club faces a battle to keep hold of its remaining top stars.
Rakitic has been in exceptional form for the La Liga club this season, scoring seven and assisting five in 13 appearances for the Andalusian side.
Those performances have reportedly piqued the interest of the Premier League contingent, with Liverpool now joining Manchester United and Chelsea scouts at the Ramon Sanchez Pizjuan.
Manchester United have a well established need in central midfield, while Chelsea could be looking to the future with Frank Lampard set to turn 36 next year.
Liverpool meanwhile have a relatively healthy stock, although as mentioned, Rodgers was looking for a creative outlet over the summer - and Rakitic certainly fits the bill.