Suarez signed improved terms at Anfield last week as the Reds attempt to keep hold of their star striker in the long term.
He was the subject of £40m-plus-one-pound bid from Arsenal in the summer as the Gunners wrongly thought that would trigger a sale, while Real Madrid continue to be linked with the Uruguay international.
However, after signing his new deal, Liverpool will be confident of keeping the former Ajax man beyond the summer - especially if he helps them claim a top-four place to secure a return to the Champions League next season.
Reports say his new deal does contain a release clause of sorts, with Premier League clubs having to fork out at least £130m to land him and overseas sides £100m.
Suarez has scored an incredible 19 league goals so far in the campaign for Brendan Rodgers' side, despite missing the first five games of the season as he served out his ban for biting Chelsea defender Branislav Ivanovic.