Following Arsenal's rejected bid of around £30 million for the Uruguayan, Suarez's agent, Pere Guardiola, spent Monday on Merseyside in discussions with manager Brendan Rodgers and managing director Ian Ayre.
There were two meetings, the first with Ayre at the club's Chapel Street office in Liverpool City Centre and then a secondary discussion with Rodgers at Melwood, Liverpool's training facility.
No transfer request was issued on Suarez's behalf, although it was made clear the 26 year-old continues to harbour concerns as to whether his career can move forward on Merseyside.
It is understood the conversations were amicable and encouraging, Liverpool holding Guardiola in high regard as they do not believe there is currently any underhand attempt by Suarez or his representatives to broker a deal behind the club's back.
Liverpool are relaxed that Suarez does not seem - at this stage at least - as eager to force through a transfer as recent interviews in Uruguay suggested.