Newcastle placed the bid on Tuesday but Bolton have turned down the opening offer.
Samuel has just 12 months remaining on his contract at the Reebok Stadium and struggled to make an impression after Owen Coyle's appointment as manager midway through last season.
The 29-year-old made only one appearance in the Premier League after Coyle replaced Gary Megson.
Since joining Bolton from Aston Villa three years ago, Samuel has made a total of 83 appearances for the club, without scoring a goal.