Senior Indonesian ministers have publicly said the deal is on hold until Australia clarifies whether it will shift its Israeli embassy to Jerusalem, with the potential move angering the world's most populous Muslim nation.
But Senator Birmingham said issues with the Indonesian version of the deal were also part of the hold up.
"There were some translation issues still being dealt with last week, in terms of the Bahasa version of the text," he told ABC TV on Sunday.
"We will get all of those finalised and then when it suits both countries, we'll get on and get it signed because it is clearly an agreement that is of benefit to both countries."
After meeting with Indonesian President Joko Widodo on Wednesday, Mr Morrison has indicated a review of the embassy site will be done before Christmas.
He announced the potential shift in the week in October before a by-election in Wentworth, where more than 12 per cent of voters are Jewish.