High street bank Alliance & Leicester has spurned an informal bid from France's biggest bank, Credit Agricole, according to press reports.
The Independent newspaper says A&L rejected a Credit Agricole offer made within the last fortnight, that valued the UK bank at almost £5.8bn.
The paper said the £13 a share offer was considered too cheap, but A&L's bosses would be tempted at £15 a share.
Takeover rumours saw A&L's shares rise 11p to £11.90 by Wednesday's close.
It is thought that A&L did not have to make a Stock Exchange announcement because the approach was informal.
The article said that there was a rival suitor in the shape of Santander, the Spanish owner of A&L's UK banking rival, Abbey.
It is reported to have talked to A&L about a takeover deal worth over £14 a share.
Alliance & Leicester has 5.5 million customers and employs 8,500 people in the UK.
It made a pre-tax profit of £547m in 2005, down 7% on the previous year when its figures were boosted by the £52m profit from the sale of its payment processing business.