Chairman Gordon Scott is understood to have flown to Spain for talks with Ross which have resulted in the former Buddies player pledging his future to the club.
Saints denied Dundee permission to speak to Ross on Tuesday but Dens Park managing director John Nelms reportedly travelled to Spain to approach the former Alloa boss on his holidays.
But Scott acted quickly to retain his manager with the offer of an improved contract, which the 40-year-old Ross is expected to sign on his return.
In a statement posted on the club’s official website, Ross said: “Following speculation regarding my position as the manager of the club, I can confirm that I remain focused on continuing to build on the momentum we created in the second half of last season.
“James (assistant manager Fowler) and I have put in a lot of hard work already and will continue to do so as we strive to prepare a squad capable of challenging in what will be a hugely competitive and demanding Championship.
“It remains my responsibility to reward the loyalty and passion of our supporters with a team which they can be proud of.”
Ross took over at St Mirren in October after leading Alloa to 10 consecutive wins at the start of the season.
The Buddies were bottom without a win in eight matches and they were 11 points adrift from guaranteed safety before the final days of the transfer window, during which Ross reshaped his squad. They only lost one more league game and eventually finished seventh.
Dundee will now have to turn their attentions elsewhere after a fruitless pursuit of a player who began his career at Dens Park.
Neil McCann left the club on Monday after a five-match interim spell in charge following the sacking of Paul Hartley. McCann took seven points from his first three games to keep Dundee in the Ladbrokes Premiership before they lost their final two matches.