The 72-year-old has been chairman since September 2009 when he replaced Sir Victor Blank, who was blamed for the troubled takeover of HBOS during the 2008 banking crisis.
Bischoff's retirement, the subject of speculation for many months, is expected to be announced in advance of the annual meeting of shareholders on Thursday.
It is understood that a replacement has not been found and the formal process of appointing a successor is only just beginning. The name of Bank of England deputy governor Paul Tucker has been repeatedly linked to the role.
Bischoff's retirement comes at a time of heightened speculation about the government's plans to try to float off the stakes in the bailed-out banks before the general election in 2015. Lloyds has been the target of such rumours ever since the government linked a bonus for its chief executive, António Horta-Osório, to selling off a stake in the bank at a price above 61p.
This is considerably lower than the 73p the City had previously assumed would be the price targeted by the government before any sell-off was possible.
Bischoff is a City veteran who was a key figure at the investment banking arm of Schroders when it was sold to Citigroup in 2000. He ended up running the entire bank in the fallout of the 2007 credit crunch. When he left Citi in 2009, he said he had always "envisioned a limited tenure".
At Lloyds, where he earned £700,000 a year, he was chairman when Horta-Osório was appointed to replace Eric Daniels who left in March 2011.
In public, Bischoff has been playing down his intention to retire. He is expected to stay until a successor is found.
The speculation about privatisation of the 39% of Lloyds owned by the taxpayer is also hitting Royal Bank of Scotland, which is 81% taxpayer-owned.
RBS managers face shareholders on Tuesday for the first time since the bank was fined for rigging Libor and its embarrassing IT meltdown. It has told the government that it will be ready to return to the private sector next year even though it is still making a loss five years after its £45bn taxpayer bailout.
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