The News understands head coach Danny Cowley has made enquiries about the wide man – although it would mean him having to cross a divide that only a handful have bravely taken in the past.
Sims is out of contract at the Blues’ fierce rivals later this month and has been released.
His availability has alerted Pompey – although they're, unsurprisingly, not the only club who are keen, with the 24-year-old enjoying a productive loan spell at Doncaster Rovers last season.
The Yeovil-born wide man made his debut for Premier League Southampton in November 2016, coming off the bench to register an assist in a 1-0 win over Everton.
However, Sims has struggled for regular first-team opportunities at St Mary's since and only featured a further 19 times.
He had two loan spells at MLS side New York Red Bulls, although the Covid-19 pandemic curtailed his second stint in the Big Apple.
The winger then joined Donny on a temporary basis for the first half of the 2020-21 season and started in barnstorming fashion.
Sims registered three goals and seven assists as Rovers sat in the promotion places.
He was widely expected move to the Championship in January, having proven himself as one of the premier attackers in League One.
However, Sims sustained a hamstring injury in December – a setback which sidelined him for two months.
It meant the ex-England youth international was sent back to the Keepmoat rather than going to the second tier for the business end of the campaign – but couldn't hit previous heights.
He continued to struggle with injury, while Doncaster's Championship bid imploded after manager Darren Moore left for Sheffield Wednesday in March and was succeeded by caretaker Andy Butler.
In total, Sims played 32 times for Rovers as they finished 14th in the table.
Still, the wide man showed he can perform at the level required for promotion when operating at the peak of his powers.
And it is understood making the switch across the M27 wouldn't bother Sims, having been on the books at Fratton Park as a junior.
Cowley is currently plotting a major squad overhaul ahead of Pompey's renewed bid to reach the Championship and needs to bolster his attacking options.
The Blues must replace Ryan Williams, who's nearing the exit door after being offered a new deal on reduced terms.