Tourism minister Reyes Maroto said the Spanish government had given UK authorities detailed assurances that they hoped could sway Westminster.
She told local publication La Sexta: "[The islands] have a low incidence rate and today [the UK] have to review their indicators.
"We are prudent because it does not depend on us. It is a decision of the British authorities, but we have given them all the arguments so that they can trust that their tourists are safe in Spanish destinations."
Travellers returning from Spain have been told to quarantine for 14 days since late July, after a rapid spike in the country's cases, and Brits have been told only to go to Spain if travel is essential.
But talks have been taking place to make the Balearic and Canary islands exempt, the BBC reported last week, citing a UK government source.
Ms Maroto said that if no exemption is given Spanish authorities will continue working with the British government to find a way for tourism to continue in future.
She added: "For us, the best news is to have the destination open with the United Kingdom, which is our main issuing market.
"We have the best protocols and are highly valued by the tourists themselves, who have transferred to their government that they feel safe in Spain."
But British authorities have indicated that no changes are likely on Monday, although quarantine measures are reviewed regularly.
A government source told the Mirror: "There is no decision made and it’s certainly not happening in the immediate future.”
Spain has nearly 110,000 active coronavirus cases - with 3,092 reported on Friday, the largest daily increase since lockdown ended.
Estimates show that Spain's tourism sector could be set to lose £36 billion this summer because of coronavirus.
The Department for Transport, which manages the quarantine list, has been contacted for comment.