The Portuguese front man bagged 17 goals last season and was named the Edinburgh club's Player of the Year after they missed out on the Scottish Premier League title in agonising last day fashion.
The Daily Record reports that Jamestown Analytics - the data system created by Brighton's owners and which has been leased to other clubs, including Ipswich, over recent years - values Braga between £8-10m.
The 26-year-old, who still has two years left on his contract at Tynecastle, has said that he wants to stay and play in the Champions League, with Hearts facing Sturm Graz in a qualifying game later this month.
However, this report north of the border insists an exit looks likely, with Ipswich said to have joined French club Lyon and Turkish outfit Trabzonspor in showing interest.
New Hearts boss Wouter Vrancken has conceded he may have to sell players this summer, saying: "For me, it's the same as in Belgium. Clubs stay healthy by developing players and selling them to bigger teams or bigger leagues. I think it's a similar model here."
Stu's verdict
Ipswich have just signed Brazilian front man Emersonn for a club-record £24m fee from Toulouse, but it's clear they want to sign another to compete alongside him and George Hirst. I'd imagine the third striker will be someone in the more experienced mould.
Callum Wilson was a prime target after his contract at West Ham expired, but it looks like he is going to join Brentford.
My understanding is that Braga, as things stand, isn't on the list of Blues targets. This report could be a case of Hearts trying to push up the price.