Napoli appear locked in a two-team race to sign the Colombia playmaker, who reportedly favours a move to Atletico Madrid.
The battle may come down to whichever club is willing to meet Real Madrid's asking price which, according to Partenopei president Aurelio De Laurentiis, is beyond reasonable.
Atletico have denied being close to an agreement and Italy international Insigne remains hopeful James will consider a switch to Stadio San Paolo.
"The doors are open for strong players, we welcome them all," the Napoli captain told Radio Kiss Kiss.
"James Rodriguez is a true number 10, he has quality and together with us he would be great.
"Those choices, however, are up to the coach and the club."
Napoli have been quiet in the transfer market to date, acquiring only centre-half Kostas Manolas from Roma and right-back Giovanni Di Lorenzo from Empoli since the end of last season.
But after two successive second-place finishes and with the defender Insigne views as the best in Europe, Kalidou Koulibaly, already on board, Carlo Ancelotti's men are continuing to aim high.
"The Scudetto is everyone's dream," Insigne said.
"In the past few years we have come close and we have been disappointed. I'm convinced that if we all play with this determination we can cause trouble for anyone.
"We know we have a great competitor like Juve in front of us, but things could change this season with the new coach [at Juve, former Napoli boss Maurizio Sarri].
"I think we are getting stronger, but we have to start off on the right foot because we have the potential to fight at the top."