BBC chief football news reporter Simon Stone
This latest development makes it increasingly likely Amorim will be in charge for Manchester United's Premier League game against Chelsea on Sunday.
That would represent a speedy process given United were not expecting to sack Ten Hag within 24 hours when the club took to the pitch against West Ham.
Providing United turn an expression of interest into an actual request to take Amorim from Sporting, it is not an appointment that would come without risk.
For starters, Amorim has never managed outside the Portuguese league. Sporting are a big club but United are on another scale. Ole Gunnar Solskjaer aside, every manager who has followed Sir Alex Ferguson had far more experience than Amorim - and the goldfish bowl that is Old Trafford eventually became too much for all of them.
There are also some unanswered questions. How much is Amorim getting paid? What is his contract length? Will there be any money to spend on transfers? How will his preferred three-man defence fit with a squad that is stacked with wingers and number 10s? Will fellow countryman Bruno Fernandes retain the captaincy? What happens to Van Nistelrooy after the EFL Cup tie with Leicester?
These will doubtless be answered over the next few days, within any formal announcement and media conference that will follow at some point.
For now, Amorim must get through what is almost certain to be his last game as Sporting boss, say his farewells and get ready for the biggest challenge of his career.