The 32-year-old had been training with the Tigers at their pre-season camp in Portugal but left on Sunday after the Foxes matched the Championship club's asking price.
The Switzerland international is now said to be on his way to Hong Kong to link up with Leicester, who are in the Far East preparing for the start of the Premier League Asia Trophy.
It is unclear whether the transfer will be completed in time for Jakupovic to feature in Wednesday's clash with West Brom, but it appears almost certain he will become Leicester's third signing of the summer.
The 2015-16 Premier League champions have already signed Harry Maguire from Hull and also Sevilla captain Vicente Iborra.
Jakupovic is unlikely to be the last new face in the squad for next season.