Lionel Messi will be looking for a hat trick of hat tricks when Barcelona take on Valencia in the Spanish league on Sunday.
Suarez has been given a ringing endorsement by one of the Catalan club's legendary players following his debut Barca goal on Tuesday - his namesake Luis Suarez.
"I am very happy. It is fantastic to achieve this record in this beautiful and important competition," Messi said.
"Messi is the greatest player of all time, football is the king of sports and he will continue to surprise everyone for a long time," Luis Enrique said.
Messi set a Champions League scoring record of 74 goals when he netted a hat-trick in Tuesday's 4-0 Group F win at APOEL Nicosia.
Messi cemented his place as the greatest goalscorer in Champions League history in typically emphatic fashion by grabbing a hat-trick as Barcelona won 4-0 at APOEL.
Messi is even with Raul Gonzalez's all-time record of 71 Champions League goals, and he could better that on Tuesday when Barcelona travel to Cypriot club APOEL.
Barcelona face APOEL with nine points from four games in Group F, a point behind leaders Paris Saint-Germain who beat them 3-2 at the Parc des Princes.
While Messi tries to break the all-time scoring mark, another record could fall in Champions League.
Thomas Vermaelen is still waiting to make his competitive debut after joining from Arsenal in the close season.
Iniesta, who sustained the injury in last month's La Liga 'Clasico' at Real Madrid, has not been included in the squad for the match.