Stagecoach had come up with an offer after a earlier £765bn takeover bid by Spain’s Cosmen family and the UK’s CVC Capital Partners collapsed.
The Stagecoach bid included an offer for the troubled rail operator to become a 40% partner in the rail and coach group.
National Express says it rejected the offer because a deal with Stagecoach would take too long, leading to higher interest payments. The operator now plans to sell shares to cut debt.
National Express has been up for takeover since July after reporting $1.7bn in debt, forcing it to give up its East Coast Rail franchise.