Despite learning that Ricardo Fuller has asked Stoke City for permission to speak with the Black Cats, Sunderland manager Steve Bruce has hinted he might be willing to head in to the remainder of the season without a replacement for Darren Bent.
Sessegnon's £5m move from Paris St Germain is close to being finalised and that will improve Bruce's options in the final third of the pitch, even though the Benin international is not a recognised striker.
The 26-year-old is more than capable of playing on the right or left of a three-man attack, while he is also effective as an attacking midfielder behind lone striker Asamoah Gyan.
It was the role of providing back-up to Gyan at Blackpool last Saturday that Richardson impressed in and, with Fraizer Campbell and Danny Welbeck also expected back to fitness within the next six weeks, the midfielder thinks Sunderland can cope without a further attacking alternative.
Richardson said: We have midfielders who can push forward and attack. I'm sure the gaffer is trying to get another striker and, ideally, we could really do with another striker in the squad. But we have Fraizer and Danny coming back in about five weeks time.
Fraizer's been out for a long time, so it'll probably take him a bit longer to get back into the swing of things.
But if the gaffer decides to go with a five-man midfield, we have the players to make a success of that.
More than three weeks have elapsed since Sunderland first made their move for Sessegnon and, after much negotiating with PSG, a deal is finally in place that will see him move on a permanent basis.
Sunderland are also still trying to conclude a deal to sign Inter Milan midfielder Sulley Muntari on loan until the end of the season.
But Muntari's high wages at the European champions have meant that talks over the terms of the loan have been more difficult.
Both players remain in the North-East in the hope they will conclude switches to the Stadium of Light before the transfer deadline, but Muntari could also face problems over his work permit.
The former Portsmouth midfielder is keen on joining compatriots Gyan and John Mensah, but he does not meet the requirements of having played in 75 per cent of Ghana's competitive games.
Muntari still, though, looks more likely to join than a striker, even though it should not be ruled out that Bruce does make a late dip in to the transfer market in the next few days.
Sources close to Sunderland insist they have cooled their interest in Stoke City's Fuller quite significantly.
The 31-year-old was reported to have been asking for £60,000-a-week to leave the Britannia Stadium and that was enough to make Sunderland think twice about signing him.
Sunderland are also understood to have been left frustrated by Stoke's determination to receive about £5m for the forward and have refuted Tony Pulis' claims yesterday they tabled an offer for him.
Fuller and Jay Bothroyd are understood to be the two strikers that Sunderland have been the most interested in since the £24m sale of Bent, while PSV's Danny Koevermans has also been under consideration.
Regardless of whether or not Bruce does add another forward, however, Richardson insists his two match-winning goals at Blackpool last week highlight he can play there when asked.
Every time I've played behind the striker, I've done well there, said Richardson.
Obviously, the gaffer knew that and put me there at the weekend, and it paid off.
Sunderland's forthcoming game against Tottenham has been selected for live TV broadcast. The game, which takes take place on Saturday, February 12 was originally scheduled for 3pm but will now kick-off at 5.30pm.