The Norway international will arrive at Ewood Park on Wednesday and remain with Rovers until the weekend.
Michael Appleton is eager to explore potential transfer options ahead of the summer, and is keen to take a look at Jenssen.
The 24-year-old has spent his entire career to date with Tromso, but feels ready to make a move away from homeland.
He is looking forward to testing himself at Blackburn, a club that harbours ambitions of returning to the Premier League in the not too distant future.
"I am really looking forward to it and it will be a big inspiration for me," Jenssen told iTromso.no.
Tromso believe a spell in England will be beneficial to all concerned, with coach Agnar Christensen happy to sanction a training spell.
He said: "Tromso have taken the opportunity to offer Ruben some new ideas before the new season starts.
"We are happy for this to happen and similar moves are going to happen several times in the future."