"We believe that a four home unions bid would make a compelling proposition for world rugby," said McKee, whose desire to host the tournament has been matched by Italy, South Africa, Australia and Japan.
Russia joined the same countries, with the exception of England, in expressing interest in the 2019 tournament.
The bidders have until May to decide whether to make a single bid or make it jointly with another nation or nations.
"Scottish Rugby is committed to ensuring that any decision it makes in respect of hosting the event in 2015 and/or 2019 is in the best interest of growing the game and leaving a lasting legacy for the sport in Scotland," added McKie.
"We've been encouraged by the support to date which is being shown by the Scottish government and other public sector partners and, over the coming months, we will be conducting a detailed evaluation of what's involved in hosting or co-hosting RWC 2015 and/or 2019."
Scotland has been a venue for World Cup games previously, in 1991, 1999 and 2007, but a semi-final in 1991 is the most prestigious match Murrayfield has held.