Versatile midfielder Spector verbally committed to his contract offer on Tuesday night and will put pen to paper upon his return from getting married in the USA.
Elliott, linked with a move to Championship newcomers Bournemouth, is yet to fully finalise the terms of his one-year deal, which includes a further 12-month option, but boss Clark is upbeat that the pair will sign sooner rather than later.
"Hopefully we can get both Jonathan and Wade tied-up very shortly because they can play a massive part for us in terms of them being experienced players," Clark told the club's official website.
"We really need to get things resolved quickly because for me as a manager I need to start planning."
Clark added: "The indications I'm getting from Wade are that he's prepared to sign and ready to sign.
"We're just waiting until it's done and dusted, although you should never say never."
Spector, who joined Blues in 2011, has made 76 appearances for the midlands club while attacking midfielder Elliott has clocked up 87 outings, scoring 14 goals, during the same period.