O'Reilly's offer is backed by private equity firm Provident Capital, which is stumping up most of the cash.
The Irish media baron already owns The Belfast Telegraph, which has a moderate unionist political stance, and it is thought that a bid that included the News Letter would not get past the Competition Commission.
When Independent News and Media bought the Belfast Telegraph three years ago from Trinity Mirror as part of a bigger £300m deal, it was reported that competition authorities only allowed the purchase when the publisher promised the newspaper's editorial integrity would not be affected.
If successful, the deal would also give the Dublin-headquartered company titles including the Donegal Democrat and Belfast News. However, Trinity Mirror is understood to want to sell all nine of its Irish titles together.
There has been suggestions that some Irish businessmen are interested in the title. These include Ulster Unionist MP David Burnside, a former publicist for British Airways, who has been reported to want to team up with Independent for a bid.
The deadline for submissions is today. Other parties thought to be interested include Scottish Radio Holdings, which owns regional titles such as the Tipperary Star and Kilkenny People, and Thomas Crosbie Holdings, owner of the Irish Examiner.
Former Financial Times Group chief executive David Palmer is also reported to have been putting together a £40m bid backed by HgCapital.
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