Sky Sports says Biabi will have a medical ahead of completing his move to Swansea City today.
The 19-year-old will join up with the U21 squad in a £150,000 deal.
Falkirk manager Peter Houston told BBC Scotland: "Botti had travelled down to Swansea and he's had his medical.
"It isn't fully done, but he is keen to join such a big club."
Born in London and of Ivory Coast descent, Biabi made his Falkirk debut at the tail end of the 2013-14 season.
He made 31 appearances last term, mainly as a substitute, scored four goals and was notoriously sent off in a Petrofac Training Cup tie in which he head-butted two Dunfermline Athletic opponents.
"I would have liked to have kept him for another season," Houston told BBC Scotland.
"Perhaps it would have been the best thing for him to develop, but sometimes these moves disappear - anything can happen, injury can happen."