Vote on Telepathy and Suggestion
In the psionics book, it states that all psionic powers are spell-like abilities. None of them have components, but some of the powers have various types of displays (auditory, visual, etc.).
And on page 139, for the psionics creature template (which is what Mindflayers have), it says that the psionic powers are manifested just like the powers that a psion would manifest.
The other issue is that both versions of the Suggestion spell (PHB, Psionics) state that the Suggestion is language-dependent. From the phb p.174, a language-dependent spell uses intelligible language as a medium for communication. That implies to me that either the "suggestion" has to be spoken aloud or it has to be understood and telepathy would be fine. Since the Psionics book knows all about telepathy and didn't mention anything about telepathy being an adequate substitute, I'm inclined to think the suggestion has to be spoken aloud.
I'm open minded and I'm not sure.
Let's put this up to a vote of the players. Can creatures that have telepathy use suggestion without speaking outloud? If enough players vote yes, than that's how I'll rule. If enough players don't vote yes, then I'll rule the other way.