Former Tottenham midfielder Kranjcar flew into Glasgow Airport on Wednesday afternoon ahead of a medical while Scotland international goalkeeper Gilks has visited the Rangers training ground.
Gilks looks set to replace Cammy Bell, whose departure was confirmed ahead of his expected move to Dundee United.
Kranjcar is a free agent following a spell with New York Cosmos and the 31-year-old is keen to finalise a move to join former QPR team-mate Joey Barton in the Rangers midfield.
The Croatian told reporters at Glasgow Airport: “It’s great being here and I’m looking forward to the possibility but we still have to wait to see what will turn out.
“Anyone who plays football or follows football knows what a massive club it is. So I’m honoured to be in talks with Rangers and hopefully we can find a way for both us to sit down and agree a deal.
“I’m really good friends with [former Rangers striker] Nikica Jelavic so I’ve obviously heard a lot about it from him.”
Gilks is another of Barton’s former team-mates having spent the last two seasons at Burnley, although he only made two appearances, both in the League Cup.
The 34-year-old won three Scotland caps during his Blackpool days and would provide back-up for Wes Foderingham.
Rangers boss Mark Warburton revealed on Tuesday that two or three signings were hopefully imminent with another to follow later in the transfer window. He is also targeting a striker and a full-back.