According to reports by various websites and the Wrestling Observer the recently WWE released MVP has no current plans to pursue a career in TNA Wrestling. The reports state that MVP left on good terms with the WWE and is set on pursuing work in Japan and Europe. The feeling amongst these reports is that working for TNA may burn a bridge with the WWE and MVP wants to stay on good terms for an eventual return.
There have been zero reports of TNA having an interest in signing MVP but I’m sure they would be open to it under the right terms.
It is interesting to note that the same sites reporting that MVP might burn a bridge with the WWE if he signed with TNA also recently reported that the WWE does not consider TNA competition.