Up until COVID-19 I would have said TPE because rightly or wrongly that is what the authorities wanted although Northern going belly up caused some perturbation to the process and EMR being asked to enter a bid to retain the route despite the split at Nottingham - I seem to recall EMR were asked to put a bid in around February time and it wasn't publicised. I assume Northern's franchise cancellation and ongoing problems means they're out and they want some competition for TPE in the bid process.
With the way things are at present, social distancing and so on I can't imagine that the appetite is there to put the training in place to transfer the route over, particularly with the Hope Valley work also being years late.
Personally as a result I can see it staying with EMR in the short to medium term until a) the Hope Valley upgrade is sorted out and b) things like crew route learning can be undertaken with a degree of comfort and common sense.
I might be wrong but I can't see a change of this size going through just at the moment when it can tick over without any need for staff training or operational amendments.
Logic isn't always apparent on railway operations, but my understanding originally was that the route would be recast once the Hope Valley Capacity Improvement Scheme was completed - in December 2018! Since then the Castlefield fiasco has added a more pressing complexity to the route. Thanks to COVID there must be concerns as to whether the latest extended completion target of December 2023 can be met.
It seems the DfT are wanting to get this route change out of the way and December 2021 is still the current target.
Rolling stock with centre doors is one factor in helping to improve punctuality. Any of the three TOCs can lease and deploy stock to provide that.
TPE want to use the 185s (although they must be expensive to run, especially in multiple) and can see fleet advantages in using them on Liverpool - Nottingham.
East Midlands would be strongly preferred to Northern by most current users. If they have been asked to tender it would be the reliabilty issue that would be the main reason any would use to base an objection. As that's largely Network Rail's responsibility the poisoned chalice can't easily be improved by TOCs any time soon.