The centre-half is currently in Sofia as he prepares for the Republic of Ireland's World Cup qualifier against Bulgaria on Saturday.
Everton, Burnley and West Brom have all been linked with St Ledger since the end of the season but the 24-year-old seems in no hurry to leave.
St Ledger told the Evening Post: "Without doubt I'm ambitious and my dream is to play in the Premier League - every footballer should be ambitious.
"It's always nice to hear speculation because it shows you have been doing well to catch people's attention.
"But I fully expect to be at Preston when we report back for training on July 1, still learning from Alan Irvine, who is a great manager to play under and be coached by. The speculation doesn't turn my head in any way."