The 24-year-old can play anywhere along the left and joined United from Vitesse Arnhem a year ago but has failed to dislodge Patrice Evra from that position.
With Leighton Baines expected to move to Old Trafford Davie Moyes has agreed to let Buttner go out on loan with Celtic favourites to sign the defender ahead of Besiktas.
Speaking after the 1-0 away to Dundee United Lennon said: “Buttner is a player who came to our attention in the last day or so.
“I have seen him play in midfield or on the left side, or off the striker.
“I would like him to play further forward through the middle. He is a really intelligent footballer with a big build, a very good footballer.
“I don’t know how far we are down the line with enquiries. I will know a bit more later on.
“We have other irons in the fire but how far down the line we are with them I don’t know.
“Teemu has signed, Nir (Biton)has signed, we are looking to get one or two more in.”
Earlier in the day Celtic confirmed the signing of Teema Pukki in a £3m deal from Schalke 04 with the striker looking forward to getting involved in Celtic’s Champions League campaign.
“I am really excited about it and I am just waiting to meet the guys and get to play on the pitch”, the Finn told the Celtic website.
“I can’t really wait to play in the stadium in front of the fans as I have heard so many good things about them.
“Celtic are a great, traditional club. There is an opportunity to play in the Champions League and I hope I can score a lot of goals but I know it´s not going to be easy to just go in the side and I will need to work hard to get into the team.”
With Buttner poised to join Pukki and Biton Tony Watt is on his way out the club on a season long loan.
Despite the interest of a number of SPFL teams Watt is believed to be keen to join Belgian side SK Lierse.