According to Sky Germany, the Nigerian striker's representatives have informed Leverkusen of his desire to move when the winter transfer window opens. A loan move is considered a likely option, with regular playing time his main priority.
The 25-year-old has struggled to establish himself at the BayArena after a frustrating loan spell at Werder Bremen and persistent knee problems disrupted his progress.
Boniface's situation has become more difficult under head coach Carles Martinez, who has left the striker out of Leverkusen's squad for the UEFA Europa League league phase.
His hopes of securing a place in the European squad suffered another setback in late October when winger Martin Terrier sustained a serious injury. Rather than registering Boniface as a replacement, Leverkusen opted to include midfielder Jonas Hofmann.
The decision underlined Boniface's current position in the squad, with the striker facing an uphill battle to force his way back into the team's plans.
Martinez and managing director Simon Rolfes have both indicated that Boniface still needs to regain the physical condition and intensity required to compete for a regular starting role.
With Patrik Schick ahead of him in the battle for the centre-forward position, Boniface faces a significant challenge to earn more opportunities unless he can demonstrate that he is ready to perform consistently.
Despite his desire to leave, there are reportedly no advanced negotiations with potential suitors at this stage. Leverkusen are understood to be willing to consider their options, including either a loan deal or a permanent transfer.