The man in charge of Lloyds at the height of the credit crunch is suing the bank for hundreds of thousands of pounds in unpaid bonuses.
Daniels is understood to be seeking around £500,000 in compensation. It is not clear how much Tate is looking for.
The move is bound to cause public outrage, given Daniels was chief executive of the bank in 2009, when taxpayers were forced to shell out around £20 billion to keep the lender afloat.
The bank has only just recently returned to the private sector after the government sold its 43% stake.
As the credit crisis unfolded in the autumn of 2008, Daniels met with then prime minister Gordon Brown and promised to save HBOS following a dramatic collapse in its share price.
After 36 hours of intense negotiations Lloyds thrashed out a deal to buy HBOS, with the purchase completing in January 2009. Absorbing HBOS put Lloyds' balance sheet under extreme pressure, with the bank forced to suspend dividend payments.
Investors were particular galled at suggestions that the then chair of Lloyds, Sir Victor Blank, had struck the HBOS deal with Brown at a City drinks party.
The deal is the subject of a £350 million shareholder lawsuit in which Daniels and other senior Lloyds managers have been named as defendants. The case is due to go to trial this year.
Since leaving Lloyds, Daniels has taken up a number of posts in the City. These include a non-executive role with leading peer-to-peer lender Funding Circle.
He also serves as an adviser to Mayfair-based boutique investment bank Stoneharbour and private equity giant CVC Capital Partners.
Tate left Lloyds a year after Daniels and in 2013 joined Australian finance group ANZ.
Lloyds refused to comment on the case. 'As this matter is a live legal issue, it would be inappropriate to comment,' a spokesperson told The Times.
A spokeswoman for Daniels declined to comment, while calls and emails to the law firm representing Tate did not get a response.