Both sporting retail powerhouses have tabled indicative offers for Evans in the last week, Sky News first reported late last night.
The bids come in addition to an offer from Britain's biggest bike firm Halfords, as well as several other financial investors. Evans is understood to have hurried up the bidding process in order to avoid collapse, as it is said to need more than £10m in fresh funding to make it through the coming months.
Evans, which is owned by private equity firm ECI Partners, has more than 60 stores across the UK. The buyout is likely to come at a reduced valuation of the business, as ECI seeks to sell to a buyer who will guide the business through tough trading conditions.
While Sky News understands JD Sports holds a genuine interest in Evans' business, it is unknown whether Sports Direct owner Mike Ashley has any intentions to progress further in the auction process.
The news comes after Ashley distanced himself from the board and senior management of House of Fraser, the chain of department stores he bought out of administration for £90m in August.
Sports Direct and JD Sports did not immediately respond to requests for comment.