Tom Cruise and Katie Holmes -- No Love Lost ... NOT on Speaking Terms

Tom Cruise and Katie Holmes want nothing to do with each other ... to the point they don't speak to one another, even about Suri.

Sources close to both Tom and Katie tell us they do not communicate at all. There are no direct co-parenting discussions. Everything regarding Suri -- visitation, child-rearing, etc. -- is handled through intermediaries.

Our sources say there are bad feelings on both sides, and no desire on either Tom or Katie's part to mend fences.

As for Suri ... sources close to Tom say he's still involved in his daughter's life, although he hasn't seen her in months because he's been in London shooting "Mission Impossible 5." Production wrapped last Thursday and our Tom sources say he's coming back to L.A. and will see Suri when he returns.

On the Katie side we're told she's dissatisfied with Tom's involvement in their daughter's life ... that it hasn't been enough.

And there's this ... we've been told there is some sort of relationship between Katie and Jamie Foxx. Our Tom sources wouldn't comment on the relationship, but say Tom has been concerned in the past with other boyfriends because of a possible negative influence on Suri.