BBC Sports reports that Barcelona director Albert Soler said the Reds put that valuation on the Brazilian on the final day of the Spanish transfer window on Friday.
Liverpool turned down three offers from the Spanish side for Coutinho, who had made a transfer request, and maintain the 25-year-old was not for sale.
The Anfield club regard Barcelona’s claim as “absolutely false”.
“Liverpool were asking for 200m and logically we didn’t accept that,” said Soler at a news conference on Saturday.
“We thank the player for the efforts he made, because he did make a big effort and showed he wanted to play for us.
“The situation ended as it ended and there is nothing else we can do.”
Barcelona wanted Coutinho after selling his Brazil team-mate Neymar to Paris St-Germain for a world record fee of £200m.
Liverpool said Coutinho was not for sale and rejected bids of £72m, £90m and one in the region of £114m prior to the deadline in Spain, which closed a day later than in England.
Coutinho, who scored 14 goals last season and spent six weeks out with an ankle injury, signed a new five-year deal at Anfield in January which did not include a release clause.
He then said he wanted to leave via email, a day before the Reds opened their Premier League campaign at Watford on 12 August.
A back injury has forced him to miss all three top-flight games this season and the two legs of a Champions League qualifier against TSG Hoffenheim, which the Reds won 6-3 on aggregate.
However, the midfielder made his first appearance of the season when he played for Brazil in a 2-0 win over Ecuador in a World Cup qualifier on Thursday, scoring the second goal.