Nope it would be less than £6Bn for the tunnel and station. For reference the tunnels for HS2 which are designed to operate at 140mph which adds to the complexity, cost around £250m per mile. You dont need more than 6 miles of tunnels so around £1.5Bn would cover the tunnels. Mainline station modifications at Piccadilly and Lyme Street you wouldnt get much change out of £500m for each station. Once you move out of the city, if you still want tunnels a cut and cover design which is much cheaper than bored tunnels could be used.
Plain line electrified railway costs around £2m per single track km so a 2 track railway so roughly 65km (giving a bit of leeway) from Manchester to Liverpool = 65km*4 tracks*£2m = £520m, stick some additional stations in they are about £40m each to design and build (lets say 5 = £200m).
Still well within the £6Bn and still plenty of fat for all the consents, land purchase etc.
That said the rate at which we sanction the construction of such projects, inflation would probably make the £6Bn become £12Bn by the time its started.