The People says agent Pere Guardiola is planning a trip to Merseyside before the end of the year for talks with club representatives about improving the Uruguayan's deal.
Discussions over his contract would give the Suarez camp an opportunity to add new clauses.
One factor certain to be discussed is a significant rise on his current financial agreement of around £120,000-a-week if Liverpool finish in the top four.
Barcelona and Real Madrid both want to sign him and, after the controversy over the £40million release clause that sparked Arsenal to make a summer bid, it is possible a new higher transfer trigger fee could be inserted.
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