The Brazil international has been a long-term transfer target for the Catalan club. The La Liga leaders' multiple approaches were turned down for the 25-year-old, despite the player handing in a transfer request to leave Anfield in the summer.
Barcelona are still keen on signing Coutinho and are planning to make a fresh approach to secure his services in the January transfer window. According to Mundo Deportivo, the Liverpool dressing room is "resigned" to losing the former Inter Milan man midway through the season.
Coutinho's club teammates are convincing him to stay at the Merseyside club until the end of the current campaign. However, the playmaker has reportedly no intention of continuing at Anfield and is looking for a switch in January.
Another report from Mundo Deportivo claims Barcelona are optimistic about completing the South American star's signing once the transfer window reopens next month. The deal is expected to be worth around €145m (£128m, $171m).
Redknapp wants Liverpool to demand Suarez as a part of the deal that will see Coutinho move in the opposite direction. The Uruguayan international left the Reds for Barcelona in 2014. The ex-Spurs midfielder believes re-signing the striker as a part of the swap deal would be "great move" for both the clubs.
"Philippe Coutinho was sensational for Liverpool at Bournemouth. The Reds should enjoy him while they can before Barcelona come calling again in the summer," Redknapp wrote in his Daily Mail column.
"Even if Liverpool receive in excess of the £138million Barcelona bid last summer, there are few like-for-like players they can buy - while bringing in a number of players is not always the best option. Instead, Liverpool should ask Barcelona to swap Coutinho for Luis Suarez.
"The striker has not been as prolific as in recent seasons and the Liverpool fans would love a returning hero. It would be a great move for both the club and the Premier League."
Suarez signed a new deal at Barcelona in December 2016. He has a €200m (£176.3m, $235.7m) release clause in his contract, which runs down in 2021. He is reportedly earning £290,000-a-week ($387,831 per week) at Camp Nou.
The former Liverpool striker has struggled this season, scoring nine goals in 13 league appearances. Out of these nine goals, four were scored in the last three fixtures. He has failed to score a goal in the Champions League, despite starting in six games. Since scoring in Barcelona's 3-0 win over Girona in September, Suarez struggled as the striker managed only two goals until the start of December.