UK transport operator National Express Group has received a revised offer of £688.5m ($1.12bn) from joint bidders Spain's Cosmen family and UK's CVC Capital Partners.
The two companies had made a previous joint bid, the deals of which were not disclosed.
The operator says the new proposal is under consideration and it will make an announcement when appropriate.
The operator has also said it could consider potential equity fundraising if the offer is not agreed on.
National Express has been up for takeover since July when the government said it could be stripped of its East Coast rail franchise following a funds crunch.
Cosmen is already the largest stakeholder in National Express with a close to 19% share.