The 35-year old Italy international hopes to further his career in England after being released by Atalanta towards the end of last season.
Rovers boss Sam Allardyce was excited about seeing Vieri improve his fitness and hoped he may be able to become a Blackburn player next season.
"He is obviously out of condition compared to the rest of the lads but joining us at this stage of pre-season shows a certain amount of commitment that he wants to try and play football again," said Allardyce.
"If he has got that desire and dedication and can adjust to the physical levels of the Premier League at his tender age of 36 then we have got a major player on our hands.
"There is no harm in my point of view in watching his progress and then seeing if there is a situation where we can have him for next season.
"He also has a desire to try and get in the Italy squad for the 2010 World Cup."