According to Diario Gol (via Luke Gardener in the Daily Star), Reds manager Jurgen Klopp is a "big fan" of the Croatian midfielder—who he would play alongside Jordan Henderson and Emre Can in the engine room—and signing Rakitic could soften the blow of losing Coutinho.
The Brazil international handed in a transfer request last week in an attempt to push through a move to Barca, but Liverpool have insisted he will not be sold, per the Liverpool Echo's James Pearce:
However, the playmaker was omitted from the Liverpool squad that beat TSG Hoffenheim 2-1 on Tuesday in the first leg of their UEFA Champions League play-off.
Meanwhile, there is confidence in Barcelona that they can still snap up the 25-year-old to replace Neymar, who recently departed to Paris Saint-Germain for £200 million, per Sky Sports News' Kaveh Solhekol:
It is clear, though, that Liverpool will drive a hard bargain if they are to let Coutinho go.
With only weeks remaining of the summer transfer window, the Premier League side know Barcelona need to find a replacement for Neymar, while they are also aware of the windfall they have received.
As a result, it would be no surprise if the Reds pushed for Rakitic to be included as part of any deal.
The 29-year-old would not be a replacement for Coutinho as he operates in a deeper role, but Liverpool have other talented attackers who could ease the blow of the Brazilian's departure—Roberto Firmino, Sadio Mane and Mohamed Salah.
Rakitic is one of the most proficient central midfielders in the world football: technically superb, hugely experienced and with a phenomenal range of passing.
He could be a huge asset at Liverpool.
In other circumstances it would seem unlikely Barcelona would allow Rakitic to leave the Camp Nou, but if he could be used to help the La Liga giants sign Coutinho, there is a possibility Liverpool could succeed in snapping him up.