Naismith has played under Sunderland's new manager, Jack Ross.
The Sun on Sunday reports Sunderland are 'stepping up a bid' for Naismith, who played under the Mackems' new boss Jack Ross at St Mirren.
And it adds Ross is trying to move out players ahead of a £200,000 move for the 23-year-old.
Naismith impressed despite Ross County's relegation last season, attracting interest from Aberdeen, Burton Albion and Plymouth, according to the Daily Record.
And his manager, Roy MacGregor, has told the Press and Journal the former Scotland Under-21 international is free to leave should he express a wish to do so, after the Staggies dropped out of the Scottish Premiership.
Even though some of them they think he could do better, many of his side's fans are growing resigned to losing Naismith to Sunderland...
Not over the top offer - but we need guys who will play for the shirt.— Al (@Sharp1Al) 11 June 2018
Too good for Sunderland!— JailEnder (@Jailender) 10 June 2018
Would be a shame to see him to go to Sunderland. He could do much better than that.— Martin MacLean (@shug_1980) 10 June 2018
There are three certainties in life: death, taxes and Jason Naismith playing for Sunderland next season.— Gordie Bryce (@GordieBryce) 10 June 2018
And one Aberdeen fans agrees with the previous tweeter...
Sunderland in so that’ll be that— TheNorthernLight (@kevinsmith2268) 10 June 2018
Could Naismith really do better than Sunderland?