Sky Media has sold advertising for Discovery's TV channels since 2006. However, it is understood Discovery has indicated to Sky it will not take up Sky's renewal offer when its current contract expires at the end of this year.
Channel 4 and Five are both understood to have tabled offers for the contract.
A deal between Discovery and Five has not yet been formally signed off, but an outline agreement is in place.
Discovery has been in dispute with Sky Media over the amount of ad revenue Sky pays Discovery under its current contract.
The dispute will move on to the High Court in November. It is understood the wrangle centres on a clause that allows Sky Media to cap the amount of money Discovery receives when its channels' commercial impacts reach a certain level.
Losing the Discovery contract would be a blow to Sky Media. Discovery is understood to account for about 10% of Sky Media's total commercial impacts.
A Five spokesman said: "We don't comment on such matters." Discovery, Channel 4 and BSkyB declined to comment.
Separately, Five is set for a further boost by agreeing a deal to join Project Marquee, a BBC-led initiative through which the corporation plans to share the technology behind the iPlayer to create a network of related sites.