Fotbalti.net reports that both clubs had scouts to watch the midfielder during Viking’s recent clash with Molde.
Reading and clubs from Germany and France are also reportedly keen on the youngster.
“I keep a good connection with Hearts and I tell them about promising and interesting players,”said Olafur Gardarson, Bjarnason’s agent to The Scotsman.
“They have one good player from me playing for them (Eggert Jonsson] and they usually take a look if I tell them about other ones.”