The Reds were linked with a move for the Portugal star earlier this week.
Sporting Lisbon's Joao Mario celebrates goal against Bayer Leverkusen.
The Reds have been busy in the summer transfer window with seven new signings arriving at the club so far.
It has been anticipated that more signings could arrive as Jurgen Klopp continues to mould his squad for next season.
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One man it appeared they had targeted was Portugal star Joao Mario, with his father claiming to Diario de Noticias that they had made a bid for their son.
And now his agent has confirmed that they did make a big money bid for the Euro 2016 winner.
"Sporting received four proposal,” he told Record.
"Inter Milan and Liverpool[came in] with values between €35m (£29.4m) and €40m (£33.7m) plus bonuses.”
France's Paul Pogba in action with Portugal's Joao Mario
It now remains to be seen if Liverpool come in with another bid for the player at some point this summer.
It would be surprising to see them do so, with the signings they have made so far adding to what was already a fierce fight for places in midfield.
However, should players leave before the end of the window then there is every chance they could return for the Portugal star.
Portugal's Joao Mario in action with Poland's Jakub Blaszczykowski