Armstrong, who has previously been linked with Celtic, has impressed this season with his performances in the Scottish Premiership earning him a number of admirers.
A combative central midfielder with an eye for goal, Armstrong has got on the scoresheet four times and looks one of the brightest talents in the league.
United are said to value Armstrong in the region of £4 million and this price tag has ruled Celtic out, meaning that it looks like a straight fight between the Premier League duo to land his signature.
The 22-year-old, who has been capped at youth level for Scotland, has been a mainstay for the Tangerines for the past three seasons and looks capable of making the step up.
Armstrong currently has 18 months remaining on his contract at Dundee United and, although their chairman Stephen Thompson has publicly stated his intentions to keep his star man, the Premier League pair are reportedly set to make offers over the coming weeks.