The 23-year-old’s contract expires this summer and BBC Sport reported in April he had agreed terms with Real Madrid.
PSG were prepared to offer the forward a 150m euros signing-on fee to keep him at the club for another two seasons.
But the La Liga champions expect him to make his decision public shortly.
Mbappe to Real Madrid – a transfer months in the making
Mbappe is set to join up with his France team-mates for Nations League games at the start of June and the Spanish club anticipate an announcement from him before then.
“Real Madrid are confident the terms agreed in the past will be respected, even though he tried to change them a bit when PSG came up with a huge offer of a 150m euros signing-on fee,” said Balague.
“Since then, the things that needed to be finalised are the image rights and other things related to the contract but Madrid insist the personal terms have been respected.
“They are confident that when he comes out with his decision before he joins up with France, it will be to say he is going to Real Madrid. Every time there has been a news story coming from PSG, the message from Real Madrid has been ‘don’t worry’.”