The 25-year-old made 23 Premier League appearances during his debut season with the Saints but only found the back of the net twice while also contributing three assists.
According to The Sun, Southampton are therefore open to the possibility of Armstrong leaving on loan for the 2022-23 season, and Watford are in pole position for his signature.
However, the report adds that Armstrong is reluctant to return to the Championship, where he scored 28 goals in 40 appearances for Blackburn Rovers during the 2020-21 season.
The Lilywhites are struggling to agree a fee with Boro, though, as the Riverside club are thought to be after at least £15m to sanction the England Under-21 international's exit.
Manager Chris Wilder has admitted that Spence's intention is to play in the Premier League, though, telling the Northern Echo: "The boy obviously doesn't want to come back here, which I've got absolutely no issue with. He obviously sees his future away from here, and he had a brilliant season last season.
"We're expecting that deal to happen, but if it doesn't, then he's our player. From a club point of view, the deal has to be right. We're not trying to stand in the way of anybody. I've never done that as a manager, and I've had plenty of situations before where opportunities have come along to players."
Spence spent the 2021-22 season on loan at Nottingham Forest, contributing three goals and five assists in 46 appearances to help the Tricky Trees return to the Premier League and reach the quarter-finals of the FA Cup.
The 22-year-old formed an effective partnership with Seko Fofana in the Sang et Or midfield last term and registered one goal and four assists in 34 Ligue 1 appearances.
According to French outlet RMC, Palace have now agreed to sign Doucoure for an initial £18m, and the fee could rise to as much as £22.3m with performance-related bonuses.
Palace are understood to have seen a £14.5m offer rebuffed before striking a deal with Lens, who had Doucoure under contract for another two years.
The Mali international has totalled eight goals and seven assists in 131 appearances for Franck Haise's side since joining as a teenager in the summer of 2018.
Reinier has spent the past two years at Borussia Dortmund, but it was an underwhelming affair for the Brazilian, who managed just one goal and one assist in 39 games for the Black and Yellow.
The report adds that the deal will be a straight loan with no option or obligation to buy, and manager Nelson Verissimo has given the green light for his side to sign Reinier.
The five-cap Brazil international is yet to make a senior appearance for Real Madrid but has recorded two goals and an assist in three games for the club's Castilla outfit.