Standard Chartered acted after the widespread condemnation which followed the Uruguay striker's refusal to shake the hand of Manchester United captain Patrice Evra, the man he had been found guilty of racially abusing, at Old Trafford on Saturday.
"We were very disappointed by Saturday's incident and have discussed our concerns with the club," the bank said in a statement.
Suarez yesterday apologised for his actions, as did manager Kenny Dalglish for his behaviour in a post-match television interview.
Managing director Ian Ayre criticised the player for misleading them over his intentions in the pre-match handshake and said the 25-year-old had been told "his behaviour was not acceptable".
The raft of statements issued from Anfield within a 60-minute period yesterday afternoon represented a significant but belated change in the way the Merseysiders had dealt with the issue since Evra first made his allegations after the match between Liverpool and Manchester United in mid-October.
Criticism of the incidents at Old Trafford spread worldwide but most notably they became news in America, where the club's owners Fenway Sports Group are based.
There has been no comment from FSG on the situation throughout the whole saga but their influence in the public pronouncements yesterday cannot be under-estimated.
The concerns expressed by Standard Chartered, who are almost halfway through an £81million four-year deal which is the most lucrative in British football, will also have been a significant contributory factor.