SOUTHAMPTON, ENGLAND - AUGUST 12: Dusan Tadic of Southampton and Leon Britton of Swansea City battle for possession during the Premier League match between Southampton and Swansea City at St Mary's Stadium on August 12, 2017 in Southampton, England.
Meanwhile Swansea were without Gylfi Sigurdsson, with the Welsh club yet to accept an offer from Liverpool's cross-town rivals Everton for the Icelandic playmaker.
Dusan Tadic then stabbed wide following a cut back, with England global Bertrand again the provider, when the goal was at his mercy.
"If that [move] does go through, then we can start acting on getting some of our targets". Abraham had an effort blocked early in the second half before Gabbiadini curled a shot wide.
It ends goalless, as Mauricio Pellegrino's side have to settle for a point on the opening day.
The Swans have failed to score in six of their 10 Premier League contests against Southampton.
Swansea were mired in a Premier League relegation fight for much of last season, with Clement's arrival in January the turning point in their campaign.
Southampton boss Mauricio Pellegrino said: "We did everything to win the game but we couldn't. We couldn't, because football is like this - sometimes with a couple of chances you can score, but today we couldn't".
He revealed: "Swansea are a good team because they have a balance between defence and attack as they play with a diamond in the middle and the full backs up high".
The Dutch defender handed in a transfer request earlier this week, and according to the Mirror will miss Southampton's opening game of the season on Saturday when they host Swansea City due to a "virus".
"We are still in a situation at the moment where there's a difference in opinion on the valuation of the player, but I don't think it's far off". Every game we play we have to try to get points on the board and look to play better.
"I'm a little bit disappointed, because we did everything to win the game".
"I think we have quality and spirit in the team".