The 21-year-old forward has been in impressive form for the Italian outfit, scoring seven goals in 21 appearances in Serie A this season.
Gunners boss Arsene Wenger has been credited with an interest in bringing the Algerian to the Emirates Stadium, and were linked with a move for Belfodil in the January transfer window.
Negotiations between the two clubs reached an impasse, with Parma determined to keep the player at Stadio Ennio Tardini until the end of the 2012/13 campaign, though Arsenal have now been offered renewed hope in their pursuit of Belfodil's signature.
"We decided that we wouldn't sell any of our best players in January," Ghirardi confirmed. "We're delighted with the offers we received, but we never thought of selling.
"Sales in June? We'll think about that, but there is plenty of time. Our players agree on the project in place here so we are happy to keep them."
Arsenal completed one January signing, completing a deal for former Malaga left-back Nacho Monreal, who arrived in north London on transfer deadline day for an undisclosed fee, reportedly around £8.5million.
The Spain international had initially been targeted to move to the Emirates in the summer, but the transfer was brought forward by Wenger, so the 26-year-old can cover the thigh injury sustained by Kieran Gibbs, signing a contract with the Gunners until 2017.