In a statement on Friday, the club's owners said its "definitive stance" was that "no offers will be considered".
Soon after the press conference, reports emerged that Coutinho had handed in a transfer request, and although initially Liverpool insisted that was not the case, it is understood they have now received one from the player.
Both clubs are fringe title challengers and former England midfielder Jenas believes that without players who act as the heartbeat of their teams, they will fade from contention.
Barcelona, already one of world football's biggest clubs, want Coutinho to replace Neymar following his compatriot's world record 222 million euros transfer to Paris Saint-Germain earlier this month.
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He scored 13 goals and assisted seven more in 31 Premier League appearances last term, helping Jurgen Klopp's side finish fourth.
Liverpool beat City at Anfield last season and then drew 1-1 in the reverse fixture, with Klopp optimistic he has a gameplan that can work against Pep Guardiola.
The gloomier elements of Liverpool's support have hardly been cheered by the pre-season thigh injury that will keep England midfielder Adam Lallana out until November.
He revealed that the 25-year-old has been absent from training "since last Friday" meaning that "he is not available" and "is also a doubt for Tuesday unfortunately". No price at which we are ready to give in.
"If we bring in players it's because I like and want them", Klopp added.
Keeping Philippe Coutinho in the face of intense interest from Barcelona would be another significant statement of intent.