Milner is due to link up with the England squad ahead of Wednesday's friendly with Hungary early next week, which further complicates matters.
Balotelli has Italian national commitments as well, although Mancini is hoping to tie up both deals very swiftly once those midweek fixtures are over.
"We are close with both players but now they are going with their national teams," said Mancini after Saturday 2-0 friendly win over Valencia.
"We hope that we can have these players by next Thursday.
"For now we have two days off and we are not going to talk about the market. Next week we will see.
"These deals could happen but we need to wait."