"I am looking for a left-back and his name has cropped up, so we are trying to do a deal there.
"I've always maintained we've been trying to get a left-back because the only recognised one we have really is Emilio Izaguirre and he's played a lot of football and at times it does take its toll on him."
Netherlands Under-21 international Buttner joined United from Vitesse Arnhem in August 2012, signing a five-year contract.
He has made 13 appearances for United, scoring two goals.
Highlights - Dundee Utd 0-1 Celtic
Besiktas could now be favourites to sign the 24-year-old should he leave Man Utd.
As the Scottish deadline approached, Buttner's agent, Aleksandar Bursac, told BBC Scotland: "Talks are ongoing and we hope that something will happen.
"It's not only Celtic, but Besiktas are also very keen. Alex favours Celtic because of the Champions League and the traditions of the club.
"We hope that United recognise that letting him go on loan would be great for his development."
However, Lennon appears to have been keen to add another striker to his squad ahead of the Champions League group stage.
Bids of around £1.2m were not enough to entice Peterborough to part with Tomlin, who they signed from Rushden & Diamonds in 2010 and who has since scored 39 goals in 122 appearances for the English League One side.
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