The 21-year-old has twice signed for PSG but is keen to leave the club after spending the season on loan at Leipzig last time around.
German publication Bild report that Manchester United are very keen on the Netherlands international and are willing to make a huge bid of €100m (£84.1m).
Bayern are also ready to make a similarly massive offer, with L’Equipe reporting that they will go up to €90m (£75.7m) for the forward.
However, Fabrizio Romano reports that PSG do not want to sell Simons and are only willing to loan him out, with RB Leipzig confident that they can bring him back to the club on another short-term deal.
Simons may have no long-term future at PSG, but the French club do not want to sell him before 1 January 2025, reports Bild, because his former club PSV would receive 20 per cent of the fee from any deal done before that date.
A loan deal with an option to buy could be secured this summer, with the permanent transfer to be completed next year.
Bayern have made no secret of their interest in Simons, with sporting director Christoph Freund full of praise for the Dutch star earlier this month.
‘He is a very good player. He had a very good European Championship and a great season with Leipzig,’ Freund said.
‘He’s developed really well. I think he’s going to have a really good career at the highest level. He has everything, mentality, character and is just an exceptional player.’
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