The Saints have enjoyed a relatively solid start to the Premier League season, but find themselves in the relegation zone heading into the New Year.
This has led to speculation that manager Nigel Adkins will look to strengthen his squad, with their leaky defence – which has conceded 37 goals – being top of his list of priorities.
Birmingham’s Butland is seen as the ideal candidate between the posts, with current number Kelvin Davis failing to produce the required level of displays.
The England international is said to be available for around £5m, with his club keen to sell due to financial difficulties.
They may face competition from Liverpool, Manchester City and Everton, who are all thought to be keen on the 19-year-old.
As well as a new goalkeeper, Adkins is also keen to bring in another centre-back, and will turn his attention to Cagliari’s Astori.
The 25-year-old Italian has been in impressive form for the Serie A side this term, attracting the attention of clubs such as Napoli and Juventus.
It is thought that a bid of £8m will be enough to persuade Cagliari to part company with one of their star men.