The 21-year-old insists he still has a lot to learn before he could move to another club.
Russell scored United’s second goal in their win over Rangers in the Scottish Cup on Sunday.
“Rangers are always going to be difficult and they worked hard but it just didn’t come off for them and we took our chances and came away with the win,” he said.
“It’s good to hear that clubs are interested in you, especially massive clubs like Celtic.
“But I think the best place for me just now is Dundee United. I’ve still got a lot to learn and hopefully I can do it here.”