Hughes was appointed as Mauricio Pellegrino's successor in March with the Saints one point and one place above the relegation zone.
Southampton went on to secure survival on the final day, despite suffering a late 1-0 defeat to champions Manchester City.
"It just feels like the right hire at the right time for the club," Krueger told BBC Sport.
"The decision to go with Mark in the time frame that we had to meet him and to bring him in was very tight, but everything since they've been here has been natural and the fit has been perfect.
"So, we're in really good conversation. We began these conversations last week and they continue here, and we will build on them."
Hughes himself admitted that he "would love the opportunity" to remain in charge of the south coast club.