The defender opted against a move to the Premier League, while Man United were wary of his recent injury record.
They were also unwilling to meet the £40million valuation of a player who missed 33 games last season through a variety of problems.
Hoeness told Sky: 'Jerome has told [chairman] Karl-Heinz Rummenigge he wants a change.
'Only Paris is an option, if they pay accordingly, then we will deal with it.
'If they do not, he will stay with us and then everything is OK. I would say the odds are 50-50.'
Since joining Bayern Munich from Manchester City in 2011, Boateng has won six Bundesliga titles and the 2013 Champions League.
The 29-year-old was a also a vital part of Germany's 2014 World Cup-winning squad, and has 74 caps.