The 25-year-old is currently with Ajaccio, but they have been relegated to Ligue 2 after a disappointing campaign.
Jabi, normally a right back, can also feature in the centre of defence and is understood to have been watched by both clubs in recent weeks.
Both Bolton and Blackburn are likely to be busy in the transfer market this summer and Jabi could be an option for both - given he is unlikely to cost a huge amount of money.
Meanwhile, Charlton have beaten Bolton and Middlesbrough to the signing of USA international defender Cory Gibbs on a free transfer from Feyenoord.
The 26-year-old told the club's official website: "In the past week I've received interest from Middlesbrough, Bolton, Reading and Charlton.
"Playing Premiership football has always been my dream and I was flattered to have such options, but having met with the representatives from Charlton I was hugely impressed with the chairman, Richard Murray, and his ambitious plans for the continued development of the club.
"I honestly believe I am joining a club that is ambitious and hungry for success."