It is believed the clubs are now in discussions over whether Rangers take Henrique on loan initially or buy him outright.
The transfer is subject to a work permit being received for the 20-year-old, who has yet to make his senior Brazil debut.
Henrique, who was voted player of the tournament at last summer's Under-20 World Cup in Colombia, has already hailed the prospect of joining QPR as "a fantastic opportunity".
He told The Sun: "I know a lot of clubs are interested in me. But when I spoke to Mark Hughes and QPR, they made me feel very excited about their plans.
"I want to go to a club with ambition and to play in London would be a fantastic opportunity.
"The manager is known everywhere. He played for great clubs like Manchester United and Barcelona.
"As a striker, I know I can learn so much from him. I've always wanted to play in Europe and, for me, England has the most exciting league in the world."
Reports suggest any loan could be for 18 months, with a permanent transfer costing around £5million.
Hughes has repeatedly acknowledged his new side's goalscoring problems since taking charge, with only Wigan having netted fewer times in the Premier League this season.
Speaking after Sunday's 1-0 defeat at Newcastle in his first game in charge, he said: "It's important that we improve our goals-for column because that is hindering us at the moment."
Hughes is also looking to bolster his defence, having made bids for both Chelsea's Alex and Blackburn's Christopher Samba.
QPR are understood to retain an interest in signing the centre-backs, who have both submitted transfer requests.