Madine is available on a free transfer after being released by Wednesday earlier this month.
Madine began this season in the Wednesday team before being sent out on loan a Coventry City and Blackpool.
The former Carlisle striker scored four goals in 13 appearances for Coventry and found the net three times for Blackpool in 15 games.
The 24-year-old is thought to have attracted the interest of a number of clubs, but Bolton are set to win the race for his signature.
Bolton boss Neil Lennon is in the market for striking reinforcements with Craig Davies and Jermaine Beckford both being released this summer and he has made Madine one of his top targets.
Madine has had something of a chequered career having had several criminal convictions against his name, including spending five months in prison of an 18-month jail term in 2013 after being found guilty of ABH and GBH in Sheffield.