Contactless Payment has now arrived on Merseyrail- https://www.merseyrail.org/tickets-passes/tap-and-go/
However, as in London, it does not support Railcards so actual tickets with railcards may be cheaper.
Note also that it does NOT apply to buses (as it does in London) nor does it work at Chester. station
If travelling to Chester from Liverpool a paper Merseyrail Day Saver at £6.40 remains your best fare, if using buses and/or the commuter ferries as well as trains a paper Merseytravel Saveaway at £6.50 is the best option.