The 11-year-old recently proved her showbiz potential when she joined mum Katie on stage at the iHeartRadio Jingle Ball to introduce Taylor Swift's performance.
Suri may have won over the crowd, but dad Tom was reportedly 'furious' at the on-stage display.
'He really thinks Suri is too young to go into show business,' a source says.
Tom also has concerns about Suri talking to the media - and what she might say publicly about him.
'The fact that he hasn't been around much since the divorce from Katie - it will cast him in a negative light,' the source adds.
For the full story see this weeks issue of New Idea - out now!