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Suarez, 35, left Atletico Madrid in the summer and returned to Uruguay to rejoin Montevideo side Nacional, where he began his professional career back in 2005.
Suarez has performed well since returning to the club, scoring four goals and providing three assists in eight games.
But the striker will leave Nacional when the Uruguayan season finishes at the end of October.
In a statement to supporters, Nacional president Jose Fuentes confirmed Suarez will depart next month.
"When the Uruguayan Championship ends, Suarez will leave, that's how we arranged his deal," said Fuentes, as reported by ESPN.
"It's what we agreed and he made a huge effort to come here.
"I say this to avoid generating fan expectations. Suarez is leaving. We've asked him, and he answered the same thing as before."
It is believed that Suarez would have preferred to remain in Europe following his departure from Atletico Madrid.
But it is not clear if the Uruguay international will look to join a new club before the World Cup this winter.
Nevertheless, some Liverpool supporters have urged the Premier League side to re-sign the striker, who scored 82 goals in 133 games for the Reds during an unforgettable three-year spell at Anfield between 2011 and 2014.
"Come back to Liverpool,” wrote one fan on Twitter.
Another added: "#LFC should give it a go. He'd come for cheap just to mentor Darwin Nunez."
While a third wrote: "Imagine Suarez Nunez up front," followed by the eyes emoji.
Come back to Liverpool— Ciaron (@Intelexcellence) September 20, 2022
Come home 🔫🔫— Owen (@OwenLFC22) September 20, 2022
Suarez's immediate focus will be on the current international break, with Uruguay facing Iran and Canada in their final warm-up matches ahead of the World Cup.
Uruguay's tournament gets underway on November 24 against South Korea.
They then face Portugal on November 28 before rounding off their group fixtures against Ghana on December 2.