The Daily Mail says the 24-year-old Scotland international, formerly of Liverpool and Fulham, has five months left on his contract and has attracted scouts from Swansea City and West Bromwich Albion in recent weeks.
Dundee United chairman Stephen Thompson said: "We did turn down a verbal offer last week. It's a very difficult one, we'd like Gary to stay. We've made him an offer to stay but there's only so much you can do.
"It's a very difficult one with Gary because he's only got about 20-21 weeks left on his contract but what difference will he make on the park in those weeks? We'll see how it goes and hopefully he's still playing here for a while yet."