City are eighth and Eriksson has already matched the club's best Premier League points tally of 52 with four games to go - starting at home to Portsmouth.
But Shinawatra this week threatened to sack the former England chief because City have won just three of their last 13 league games.
Eriksson said: "It would have been better not saying that at this moment.
"Only recently I heard Dr Thaksin say that a top 10 finish this season was the goal. Well, we are well on track for that.
"I admit the second half of the season has not been as good as the first. Maybe we did too well at the start!"
Eriksson agreed a three-year 'project' with Shinawatra when he took over last summer.
But Valencia have been alerted to the Swede being unsettled at City and are prepared to top the £2million-a-year wages Eriksson earns at City.
They have just won the Copa del Rey and are sure of a place in the UEFA Cup next season.
But coach Ronald Koeman is heading for the sack this summer after a disastrous La Liga season which has left them just five points off the relegation places.