Lloyds TSB is reviewing its relationship with motor underwriting partner Churchill.
A spokeswoman said: "We are talking to Churchill about whether to renew the contract which runs out later this year, or to go out to tender."
She said that LloydsTSB was not concerned that Churchill was now owned by rival Royal Bank of Scotland.
Alliance & Leicester, which also sells Churchill policies, said that it was keeping an eye on the situation and would be watching for developments.
Nationwide Building Society said that it was happy with current arrangements with home and motor cover supplier Churchill and that it would not be changing its stance because of the takeover.
The Co-operative Bank dropped Churchill after being pressured by sister company Co-operative Insurance Services, a spokesman said.