A year ago an Ajax team that reached the Champions League semi-finals - and came within a whisker of making the final - was broken up as Frenkie de Jong was sold to Barcelona and Matthijs de Ligt to Juventus.
Left-back Tagliafico, 27, is the most likely to depart and the Argentina international is thought to be interesting both Chelsea and Arsenal.
"The transfer market will start in August - the top leagues are now being played out, so the money flows are maintained," Ten Hag told Het Parool.
"The market value of players will be slightly depressed, but not much. Based on their performance and ambition, a number of our players also want to make the move abroad.
"Agreements have been made with Andre Onana, Donny van de Beek and Nicolas Tagliafico, but it remains to be seen whether the market is indeed breaking loose.
"For Onana and Van de Beek, another year of Ajax could certainly be an option, for Tagliafico it is slightly different because of his age."
Another Ajax youngster on the radar of Europe's major clubs is Sergino Dest.
Bayern Munich have been linked with the Netherlands-born teenage defender, who has already represented the United States at senior level, but Ten Hag would rather the 19-year-old continued to develop with Ajax.
"I can only argue why he should stay," he said.
"I know how it is. If I can't convince him and the right price is paid, I can't rule out going. In general, I say you have to make the step abroad if you are ready for it. If you go too young, there is a chance of failure.
"The culture and structure in which you grow up is your support. In order to stay upright in another country, in another competition, at the age of 20, you have to do a lot."