Four train-makers - Adtranz, Bombardier, Siemens and GEC Alsthom - have lined up to bid for the lucrative deal, which industry insiders say would be worth more than pounds 300m.
With the announcement of the preferred bidder to be made this week, executives could see the value of the contract increase by up to 25 per cent.
If Richard Branson, the chairman of Virgin, commits his company to the order - which would be in addition to the 55 high-speed trains for his West Coast operation - it would make him the "tilting train tycoon of Europe".
Managers at Virgin have been attracted by the huge time savings tilting trains would provide. Calculations suggest the twists and turns of many of CrossCountry's routes would see significant journey time reductions.
For example, the trip from Birmingham to Bristol, which can take more than one and a half hours, could be cut by 30 minutes.
The other advantage of tilting trains is that they allow higher frequencies on many routes. One lucrative service that would benefit is Birmingham to Manchester.
Any tilting train order for CrossCountry would seem to favour Adtranz and GEC - as both are also bidding to build tilting trains for Virgin's West Coast service. However industry sources point out that Virgin could lose out if it only chose one supplier.