The Mexican was the first driver to test positive for Covid-19 last Thursday, which ruled him out of the weekend's British Grand Prix.
"I'm fine thank God. I haven't had any symptoms," Perez, who has been self-quarantining, wrote on Instagram.
"This is how I've spent my days - training, iPad, TV, phone and kitchen. Yes, they've been long days.
"Looking forward to coming back very soon."
Perez was replaced by German Nico Hulkenberg last weekend, but the former Renault, Sauber and Force India driver was unable to compete at Silverstone as his Racing Point would not start in the pits before the race got underway.
Hulkenberg is likely to get a second shot to return to the sport this weekend in the F1 70th Anniversary Grand Prix at Silverstone, partnering regular driver Lance Stroll, with Perez expected to return the following weekend in Barcelona if he passes two coronavirus tests.
However, Racing Point have not yet confirmed their driver line-up due to the uncertainty over when Perez is able to return, having submitted an inconclusive test last Wednesday before a confirmed failure on Thursday.
“There was a little bit of confusion because it was on that cusp,” said Racing Point team principal Otmar Szafnauer. “The inconclusive test was only inconclusive by FIA standards. By (Public) Health England standards that inconclusive test on Wednesday would have been a positive.
“So you could look at it and say, well, it’s the (Public) Health England standards and therefore a positive on Wednesday already. On Wednesday you had to quarantine for seven days. The 10 days that came in the following day may or may not be retroactive. That’s the bit I don’t know.
“So we’ll ask that question of (Public) Health England and whatever they say, that’s what we’ll do. We will comply with whatever they deem is right in this situation. But I think the ambiguity comes in because it was just on that transition.”
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