Sunday's stalemate leaves Swansea one place and one point above the Premier League relegation zone.
Swansea's games this season have had more Prem goals than any other team - 99.
Fabio da Silva was forced off with a head injury, having appeared to be briefly unconscious when he landed awkwardly following an aerial challenge with Leroy Fer, and Sigurdsson drew another stop from Valdes while Boro were temporarily reduced to 10 men.
"We are very together as a town and we'll fight until the end to stay there". Sigurdsson raised speculation of a move while he was away on global duty, even though he extended his Swansea contract last summer until June 2020.
Managerless Boro attacked once more through Adama Traore whose clever pass unlocked Swansea's backline and sent Negredo through on goal, however, the Spaniard's woeful first touch let him down and the chance had gone.
On 24 minutes Valdes got lucky when he tried to punch clear a Gylfi Sigurdsson free kick from the right, but pushed the ball against his own defender before quickly diving on it.
Steve Agnew was able to reflect on a first point in his second game since taking over from Aitor Karanka at Middlesbrough.
"What I see in Gylfi is someone who is very motivated to play well here and to keep us in the league. When I was growing up in Ghana, it was always my dream to play here", he told Jack Magazine. It is possible, but I don't think he would be 100 per cent fit as he has not been training.
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"But I always tried to do my best, that's the truth, and I hope people could see that".
Arsenal's principal targets are thought to be a left-back and a centre-forward but Gibson is a left-footer which makes him an attractive option - and he can also operate at full-back.
"But we shouldn't worry about this. Our focus is on Middlesbrough".
"The budget implications are massive and we have players who will want to continue to play at the top level - whether that be here or in another country".
Clement is due to meet Swansea's American owners Steve Kaplan and Jason Levien next week.
The businessmen will attend the home games against Middlesbrough and Tottenham on Wednesday and meet with Clement to discuss future plans.
"I've done a list on where the teams are and who has got who in the run-in", head coach Clement said of the relegation battle.
Swansea's Gylfi Sigurdsson looked the player most likely to make something happen, but a thumping effort from outside the area was saved spectacularly by Victor Valdes on 64 minutes, while a free kick by the Iceland global flew just wide four minutes from time.
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