McGinn plays for Aberdeen in the Scottish Premiership, and scored seven times and provided 17 assists for them in 2014/15.
The Aberdeen Press and Journal report that the two sides are both showing an interest in McGinn, who the paper speculate could cost in the region of £500,000.
McGinn is known to managers of both clubs, and their old connections could battle to win the race for his signature.
Bolton boss Neil Lennon knows McGinn from his time as manager of Celtic. The 27-year-old spent three years with Celtic, signing under Gordon Strachan in 2009.
McGinn struggled to hold down a regular place under Lennon, and was released in 2012, but not before going out on loan to League One side Brentford.
They were managed at the time by Uwe Rosler, who was appointed as Leeds United head coach just last week.
McGinn, who has a contract at Aberdeen until 2017, played 41 times for Brentford in 2011/12, scoring four times and providing five assists. That was more appearances than he made for Celtic, 36 in all, scoring six goals.
Since signing for Aberdeen, McGinn has established himself as a key player, scoring 42 goals in 127 games, with 27 assists for the Dons.
Both Rosler and Lennon will have to convince him they can provide a platform for him to continue his success at their current clubs, and if he is able to then he could turn out to be one of the best buys of the summer.