The LPI is an independent professional league launched in January without recognition from world governing body FIFA or the Football Association of Indonesia (PSSI), which has banned the tournament's players from representing their national team.
Singapore national team captain Shahril Ishak and defender Baihakki Khaizan resigned from the PSSI's Persib Bandung to join the Chiefs and Medan had hoped their presence would convince the Football Association of Singapore (FAS) to accept their application.
"We were discussing the possibility of participating in the Singapore Cup internally. So far, we have not submitted any formal application," Medan Chiefs CEO Sihar Sitorus told Reuters on Wednesday.
"The idea came to mind when we realised that we have five players who recently played in the S.League. So, we thought it would be good to have a reunion with the people in Singapore."
However, the FAS explained that because Medan are not competing in a FIFA-recognised competition any application would be rejected.
"FAS would only extend an invitation to foreign teams to participate in any of our competitions, if these said teams are affiliated to the member associations of the country the foreign team is based in compliance with FIFA Regulations," an FAS official told Reuters on Wednesday.
"All such invitations to foreign teams are channelled through the member associations as these associations would have to give their official consent to the participation of their affiliates in overseas competitions or matches."
The Singapore Cup features 16 teams - 12 S.League clubs and four foreign sides. The 2010 competition was won by Thailand's Bangkok Glass and also featured Kitchee FC (Hong Kong), South Melbourne (Australia) and Phnom Penh Crown (Cambodia).
