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Paphitis said: "Myself and Mark McGhee spent quite a few hours with Dennis.
"We had a long discussion about his past, his future, his present, and his conclusion was that he would love to join Millwall.
"We shook hands on the deal and he will hopefully be putting pen to paper on Tuesday after he's sorted out a few legal issues, which he is trying to clear up now, with regard to registration and things."
Leicester terminated Wise's contract after he fractured team-mate Callum Davidson's jaw on a pre-season tour of Finland.
The Football League originally ruled that Leicester could only fine Wise two weeks' wages for the incident - but the decision was over-turned by an appeals tribunal on Wednesday.
Millwall boss McGhee said: "There are still one or two personal issues to sort out. He will not be with us in time to play against Walsall but he will join us and sign on Tuesday.
"We have been on the case over the last two weeks but with his appeal going on we've had to wait. As soon as we knew the result we met with Dennis straight away.
"I'm sure the supporters will be looking forward to seeing Dennis in a Millwall shirt.
"There have been a lot things going on but he wants to get on with football and get on with his life - and we can take advantage of that.
"We can make him welcome and the fans will make him welcome. If he comes and wants to see out his career here that will do for me.
"Dennis Wise wants to play football and get back into a competitive team.
"With the players that we have missing I think it is a massive signing. I think it is a bargain, Dennis is a quality player."