'The Voice' coach, who will appear on the show again this month, is known for talking about his friendships with the late singers and says Elvis didn't like it when he recorded Frank Sinatra songs.
Speaking to radio station Magic 105.4, Tom said: ''I knew Frank Sinatra and Elvis Presley very well.
''I did an album of Frank Sinatra type things and Elvis listened and said, 'Tom I heard that thing' and I said ... 'Yeah and?' Elvis said, 'We leave that to Frank Sinatra, we don't go there'.''
But the 73-year-old star said Frank was complimentary about people comparing Tom to him and wanted him to step into his shoes, as long as he didn't record rock music.
Tom recalled: ''Then, when I do something a little more rocky, Frank would say: 'Tom, when I go and they [management] ask me who could replace me, I say you! So don't go making records like that!'.''
He often finds it difficult to guide contestants on 'The Voice' after having received different opinions about his own music from the likes of Sinatra and Elvis.
Tom added: ''So, if they feel that strongly about what they feel I can do, what am I going to say to these people that come on [to The Voice]? ... You think which way do I try to guide this person?''
'The Voice' will start again on Saturday (11.01.14) on BBC One at 7pm.