De Telegraaf says Ajax want to sign Blind in the next 48 hours.
Both clubs recognise it would be best to settle terms for Blind before United leave for the US on Monday. If nothing is agreed, it's unlikely United would leave Blind in the UK.
Ajax and Blind are finalising terms over a deal to 2021 or 2022, while United are also softening their initial €17m asking price.
The 28 year-old has made it clear he'd welcome a return to Ajax of terms can be struck.