It'd be nice to know what the golden passenger level number is for Liverpool to be "at that level". Krakow has a rail link and that's as similar size to Liverpool. In fact, it was quite a bit smaller till relatively recently (increased 18% in the last year, pretty impressive).
There are other factors other than passenger numbers too, such as the feasibility & cost of the infrastructure and whether non-airport passengers may find it useful. On that latter point, Liverpool would benefit from a swathe of the fairly densely populated Speke estate being able to use it as an alternative to the rather slow 86A & 82 buses to get into the centre. In fact, it would probably be mostly local traffic but linking the airport would certainly be a delicious bonus.
How you would go about it is another thing. I've read many different ideas how to do it, all with their advantages and drawbacks. One possibility could be a connection to the WCML east of the Speke estate, going around the perimeter and finishing on Hale Road, maybe near the foot of Western Avenue. This would allow direct services from Lime Street with interchange at South Parkway for Merseyrail & the CLC. It could pick up West Allerton & Mossley Hill too, perhaps increasing service frequency at those stations. It could also allow direct services from the other direction from Crewe or Chester. A big drawback would be not being able to have direct services from the Warrington/Manchester area. Also, going round the eastern flank of the Speke estate would be a bit round-the-houses but I would imagine still competitive.
Another option (and one Merseytravel has considered) is a tram-train option. It would go down the WCML and then go onto a tramway after South Parkway. I'm not quite sure how the alignment would be achieved between South Parkway & Speke Boulevard but beyond, Speke Hall Avenue is a wide dual carriage way with a large median. You could slot a light rail line down one side. You could probably keep all the lanes of the existing dual carriageway by narrowing the median. This may well be cheaper than the heavy rail option and it would be a more direct route than going round the back of the estate. There would also be scope for an intermediate station on the light rail section near Speke Boulevard. It'd probably be a dedicated 'metro' line into Liverpool and so no direct services to other towns and cities but there'd be interchange options at South Parkway & Lime Street.
Connecting it to Merseyrail is slightly tougher as the line doesn't pass as close as the WCML. Like I said up thread, a tunnel under Woodend Avenue would be optimal but probably expensive. Nonetheless, having the airport as a southerly destination on the Northern Line would add balance to the top-heavy configuration of the existing line. Merseyrail would allow interchange for regional passengers at South Parkway but those coming in on the Chat Moss would have to get from Lime Street to Central.
I've seen other people argue for captive people mover type solutions going back and forth between South Parkway and the airport. The problem with this is that it offers no direct journeys as everyone would have to change at South Parkway. This would make it less attractive and would entice less Speke folk to use it to get into town rather than just use the bus. Also, those coming in from the Chat Moss route would have to change onto another train towards South Parkway and then onto the people mover. A bespoke people mover probably wouldn't be as good value for money either and would have specific maintenance requirements.
I would think out of those options that the tram-train would quite possibly come out on top (especially as it's the option Merseytravel have considered) but the struggles in South Yorkshire don't inspire confidence.
