The Tigers remain deep in relegation trouble inside the Premier League drop zone after their game in hand resulted in a 2-0 home defeat by Aston Villa.
That means victory over the Black Cats this weekend is a must if they are to give themselves a chance of staying up.
Turner, who joined Sunderland from Hull for an undisclosed fee during the summer transfer window, is keeping everything crossed for the club at which he spent three years, although there will be no room for sentiment for the 26-year-old on Saturday.
He said: "Things look tough for them at the moment, but they have to pick themselves up and concentrate on staying up.
"They have still got everything to play for, and that includes the game against us.
"I would like them to stay up - I have got friends still there and I would like to see them stay in the Premier League.
"I have moved on now, though, and all my focus is on Sunderland and getting us as far up the table as possible."
Steve Bruce's men mathematically confirmed their own presence in next season's top flight with a 2-1 win over relegation candidates Burnley last weekend, and are likely to end the campaign in a comfortable mid-table position whatever happens over the next three weeks.
However, their blistering start had the more optimistic of Wearsiders dreaming of Europe, and like his manager, Turner knows things could have been much better but for a 14-game winter run without a league victory.
He told the Sunderland Echo: "We had a tough time of it in the middle of the season, and that was disappointing after spending the first half of the season in the top half of the table.
"We had hoped to be higher at this stage, but the good thing is that we have turned our form around in recent weeks and I have really enjoyed being part of a good run of games where we have scored goals, won games and defended well.
"It has really put a spring back in people's step and what we want to do now is finish the season strongly and go into the close season in a really positive frame of mind.
"We know it won't be easy with our last home game being Manchester United and the other two away from home, where we haven't done ourselves justice.
"But it would be nice if we could get a few more points on the board in these last few games, and we will be looking to use the Hull game to push ourselves higher up the table."