Boeing Business Jets has already begun pitching a VIP variant of the re-engined 737 Max - the BBJ Max - to potential customers for 2018-19.
Capt Steve Taylor, president of Boeing Business Jets, says: "We are working with several existing customers and one would like to be the launch customer for that aircraft."
The CFM International Leap-1B-powered Max will begin to roll off the production line in 2017. Taylor notes that a BBJ customer typically wants a much shorter lead-time for delivery post-completion than Boeing can offer for the BBJ Max "so it takes a fairly special customer to be ready to commit to 2018 or 2019".
He says: "There are several long-term BBJ customers who'd be ideal buyers for that and we have started those conversations."
Taylor says the BBJ 2 Max - the VIP equivalent of the 737-8 - will offer a potential range of 6,200nm (11,470km).
Boeing's VIP airliner division plans to deliver a further 11 aircraft into completion centres this year - seven more 747-8s and four BBJs.
It also hopes to sell three former 787-8 test aircraft to the VIP market. Although it has 12 VIP 787s in its backlog, delivery will not begin until 2014.