The midfielder is on the verge of leaving Pompey for the Keepmoat despite being offered fresh terms.
The Blues turned down activating an option for an additional 12 months in Close's contract and instead tabled him a new two-year deal.
However, that would be on reduced terms – and he's instead explored other possibilities as a free agent.
He's pencilled in for a medical at the Yorkshire outfit today. Should that go smoothly, he could be officially announced as Rovers player shortly afterwards.
It'll spell the end of Close's time at his boyhood club. He came through the ranks at Fratton Park, making his debut as an 18-year-old in a 3-1 win over Yeovil in September 2014.
In total, the Southsea lad has made 190 appearances for Pompey, scoring 19 goals. He helped the Blues claim the Checkatrade Trophy at Wembley in 2019, as well as successive League One play-off finishes in 2018-19 and 2019-20.
Close becomes the second academy product to turn down the chance of remaining at Fratton Park this summer.
Jack Whatmough also rejected a fresh contract to instead join Wigan Athletic.
What's more, Close's exit leaves Danny Cowley with no centre-midfielders under contract ahead of the 2021-22 season.
Captain Tom Naylor has also been offered a new deal, although – like Close, Whatmough and Ryan Williams – it is on reduced terms.
Meanwhile, Andy Cannon departed at the end of his contract.
Bryn Morris was unsurprisingly released this summer. He spent the second half of the season on loan at Northampton, who were relegated to League Two.
Cowley is hoping to bolster his engine room, with Scott Twine one name on his shopping list.
The 21-year-old has turned down fresh terms at Swindon after they failed to avoid the drop from League One.