The Gers will do business in the summer transfer window, and a new goalkeeper is expected to be a priority, with Allan McGregor tipped to retire.
Ross McCrorie has been involved in recent games, while Jon McLaughlin is also on the books, but the Gers have been heavily linked with wanting Butland.
The record 55-time Scottish top-flight title winners have been in talks with English goalkeeper Butland and he is a strong contender to replace McGregor as the number 1.
However, Manchester United, where Butland has been on loan from Crystal Palace, are claimed to have made him an offer which is double that put on the table by Rangers.
The Light Blues are linked with several players ahead of their potential squad overhaul and they were expected to wrap up a deal for Butland soon.
The Manchester United loanee was also claimed to be keen on Rangers move in search of regular football, as he is yet to make an appearance for the Red Devils after his loan move from Crystal Palace.
It remains to be seen whether he accepts the lucrative offer at Old Trafford to play second fiddle to de Gea and Henderson or moves to Scotland to see himself in front of the net regularly.