Uruguay and Liverpool striker Suarez has been offered a short-term move to Kosovan club Hajvalia while he serves his ban.
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Suarez is to serve a four-month suspension from all football after being charged by FIFA for biting Italy defender Giorgio Chiellini.
And Hajvalia, who won last season's Kosovar Cup and finished sixth in the league, have made an opportunistic offer to take the forward on loan.
With Kosovo not yet recognised as a full FIFA member, the club believe Suarez's ban would not extend to the country's league -- although financial considerations would still need to be overcome for the ambitious deal to become a reality.
Director Xhavit Pocolli told Kosovan daily Sport Plus: "Suarez can't play in the next four months. As we are not part of FIFA yet, I think he can play in Kosovo, so we have an offer that we will send to Liverpool.
"We offered 30,000 euros (24,000 pounds) and a salary of 1,500 euros (1,200 pounds) for each month. This might sound ridiculous to him, but that is all we can do.
"If he is willing to come and play for us, he is welcome. As we are not part of FIFA, it would be ideal for him."
Meanwhile, Barcelona have insisted they still have funds to spend this summer, amid rumours of interest in Liverpool's Suarez.
Barca have already spent 42 million euros (33.6 million pounds) on midfielder Ivan Rakitic from Sevilla and goalkeepers Marc-Andre Ter Stegen and Claudio Bravo from Borussia Monchengladbach and Real Sociedad respectively, but received around 30 million pounds in the sale of Cesc Fabregas to Chelsea.
The club's economic vice president Javier Faus insists there is plenty more money to buy the players coach Luis Enrique targets.
"In the last three years Barca have been earning money and reducing their debt at a large rate and are stronger financially," he said.
"We can realise all the sporting challenges and signings our coaches and sporting director want."
Information from the Press Association was used in this report.