The 35-year-old is due to become a free agent upon the expiration of his contract with Nacional, which is set to run out at the end of the calendar year.
Suarez's boyhood club do possess the option to extend his stay for another year, but the Uruguay international is expected to become a free agent next month.
Despite his advancing years, Suarez is not expected to be short of offers as he prepares to end his second stint at Nacional, where he initially made his name at senior level.
Suarez is currently away with the Uruguay team preparing for the 2022 World Cup in Qatar, but speculation surrounding his future is starting to hot up.
According to transfer expert Fabrizio Romano, Suarez was recently approached by Gremio, but the experienced striker has turned down the chance to join the Brazilian club.
Romano adds that Suarez has "different plans" for his next career move, although it is unclear where the 35-year-old believes his future lies at present.
Suarez initially represented Nacional between 1998 and 2006, playing four games for the club at senior level and failing to bag a goal or assist before signing for Groningen.
Following the expiration of his contract with Atletico Madrid at the end of the 2021-22 season, Suarez returned to his boyhood club for a second spell and continued to find the back of the net at an impressive rate.
Suarez has scored eight goals and provided three assists in 16 appearances in the 2022 campaign, helping Nacional win the Uruguayan Primera Division title.
The South American came up with two goals as Nacional beat Liverpool FC Montevideo 4-1 last month to secure the title, adding to the six goals he scored in 13 regular-season appearances.
Suarez's 2022 Uruguayan Primera Division title represented his 20th major trophy at club level, having also won five La Liga titles and the Champions League during his time in Spain.
The former Liverpool and Barcelona man is the most experienced player in Uruguay's World Cup squad with 134 caps - second only to Diego Godin's 159 - while 68 goals at international level is a national record.
Suarez will be competing with the likes of Darwin Nunez, Edinson Cavani and Maxi Gomez for starts in Qatar as Uruguay prepare to meet Portugal, Ghana and South Korea in Group H.
Diego Alonso's side will open their bid for World Cup glory against South Korea on November 24 at the Education City Stadium.