And Mitchell, who sold his share in Cherries last month, is expected to have further discussions with Robbins and Poole vice-chairman Chris Reeves in the next few days.
Dolphins have been ‘homeless’ ever since being kicked out of Poole Stadium in 1994 and have a lease on their current ground at Tatnam until 2024.
Mitchell, who was responsible for reviving Cherries’ off-field fortunes during four years as chairman, said he had already drawn up a design for a new stadium for Poole.
Robbins told the Daily Echo: “Eddie has been very supportive so far and there is no reason to believe he won’t be in the future. He is the sort of chap who likes to have a scheme. He did very well at Bournemouth and I think he would do very well for us.
“Our hands are slightly tied because, geographically, there are not many areas of land in the borough that we could go for. But with Eddie on board, it does give us that little extra push and bit of flair.
"Perhaps we have gone down the same old road for too long and maybe we should look around a bit more. But it is very difficult because all the avenues we could explore, we have abandoned in the past due to finance.
“Eddie may possibly be able to bring some more investment to the club, rather like he did with Bournemouth which was fairly moribund when he took over and look at it now. I am not saying we will find another Maxim Demin but it would be nice if we could.”
Robbins added: “I think we have got to stay in the borough. The people of Poole would expect us to play in the borough of Poole and we wouldn’t want to play in Wimborne or Bournemouth. An out-of-town site very close to Poole would be acceptable but they are few and far between.”
In the meantime, Robbins said the club would continue to carry out ground improvements to Tatnam in order for the club to satisfy Football Association grading criteria for the Southern League.
Poole banked £15,000 in prize money from their FA Cup run this season before being eliminated by Staines in a fourth qualifying round replay in front of a crowd of 935 at Tatnam on Tuesday.
Robbins added: “It keeps us firmly on the map where we have been for a number of seasons. Everything is going in our favour at the moment apart from this one result.
“We were very encouraged by the crowd and the game went off without a hitch. We were just disappointed we didn’t go through.”