Both clubs could make a formal approach for the France international next summer, providing that the attacker does not agree to extend his contract past 2022.
However, Johnson feels that PSG will be successful in eventually fending off interest from two of their European rivals.
Speaking to Sky Sports News, Johnson said: "There's been a longstanding interest in Mbappe from Liverpool and Real Madrid. However, I don't see PSG giving Mbappe up easily.
"I think if they need to they would probably allow him to enter the final 12 months of his contract in a bid to try to persuade him to extend his stay with the club, particularly based on their performance in the Champions League last season.
"Kylian Mbappe is the future for this PSG project and I just don't see them giving him up without a fight. I don't think either of Real Madrid or Liverpool would be able to pay what PSG would even consider just to go to the table and negotiate next summer."
The 21-year-old has contributed 92 goals from 116 appearances for PSG since August 2017. body check tags ::