Both Everton and Wolves are said to be tracking the teenage midfielder ahead of his youth contract expiring this summer, while two more Premier League sides, Southampton and Brighton had January offers accepted (The Bolton News).
And speaking to the same publication this week, Parkinson blamed Bolton's ownership uncertainty for the ongoing delay in talks.
"The last dialogue I had with Luca’s agent he said if the club got new ownership and it was in a stable position that Luca and his family would love him to sit down and talk to us about a contract," he said.
"But we haven’t been able to get to that situation and so you can probably understand them sitting back and waiting."
Bolton's relegation could be confirmed this weekend, but while a move to Everton, Wolves or another Premier League club is likely to appeal more than a stay in the second or third tier, Connell has been advised to go somewhere he will play.
"He has had that taste of first team football," added Parkinson. "Hopefully he will stay with Bolton but if he does move on I hope it’s somewhere he will play because I always think it’s difficult when you have been in and around it to take a step back.
"He’s a mature kind of lad, his approach to the game."
Liverpool-born Connell, an under-19 international for the Republic of Ireland, has played 10 times for Bolton this season.
Should Connell choose Everton or Wolverhampton Wanderers if he is to leave Bolton this summer?