Southampton have signed Victor Wanyama and Virgil van Dijk from Celtic in recent years.
According to the report, the Saints would have to pay about £10 million in order to secure the services of the 25-year-old midfielder.
It has also been reported that Celtic will not sell the Scotland international until the Champions League qualifiers are over.

Armstrong was one of Celtic’s best players last season, and the 25-year-old would be a good signing for Southampton.
The former Dundee United star has proved himself in the Scottish Premiership, and it is only logical to expect him to move to the Premier League at some stage of his career.
Southampton have done business with Celtic before. The Saints signed defensive midfielder Victor Wanyama – now at Tottenham Hotspur – in 2013 and defender Virgil van Dijk in 2015 from the Glasgow giants.
The Saints will be aiming to finish in the top 10 of the Premier League next season, while Celtic will be favourites to clinch the Scottish Premiership title.

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