Kosovo is not covered by Suarez’s worldwide suspension as it is not an official member of UEFA or FIFA so Suarez could theoretically play in its Super League.
Kosovo side Hajvalia made the proposition in a letter to the Uruguayan’s Premier League club Liverpool.
“It will be a huge step for us to be able to have such a renowned footballer in Kosovo,” Hajvalia’s president Xhavit Pacolli told AFP.
“It will mean a lot not just to us, but to Kosovo as a whole,” he said.
Pacolli said his team could offer 1,500 euros ($2,048) per month, while Liverpool would be compensated with 30,000 euros for the four months Suarez would play in Kosovo.
“This amount might seem comical for him but this is the most we are able to offer,” Pacolli said.
He added that the offer “has a much bigger importance for us than for him.”
“We hope that he would accept to play here at least one game, just to show us what world class football is,” Pacolli said.
Hajlvalia, sixth last season, is based in a suburb of the Kosovo capital Pristina.
It is owned by music producer and millionaire folk singer Mehedin Pergjegjaj.
Kosovo unilaterally declared independence from Serbia in 2008. Although it has been recognised by more than 100 countries, it has yet to win its spot in a number of international organisations.
Uruguay has not recognised Kosovo.
Suarez was sent home from the World Cup for biting Italy’s Giorgio Chiellini in Uruguay’s final Group D match.
He was given a total four-month ban from football on top of a nine-game international suspension.