Bellamy has been out since November with a knee injury but is in the squad for Saturday's visit of West Ham - Solskjaer's first home game since since replacing Malky Mackay.
The 34-year-old quit international football in October and his current deal is up this summer, but Solskjaer hopes to persuade him to stay on.
"Craig's been training with us for a week and he's looking really sharp," Cardiff's new manager said. "He'll be involved and in the squad.
"We've spoken together and I gave him my thoughts: play as long as you can if you feel you can justify your performances.
"It's my job now to get him performing and back on the pitch, hopefully I'll motivate him and inspire him to prolong his career."
Solskjaer made former Manchester United reserve Magnus Wolff Eikrem his first signing this week and continues to be linked with a move for another ex-United player - Hannover striker Mame Diouf.
Mats Moller Daehli, a midfielder at Solskjaer's old club Molde, is another reported target.
Asked about Diouf and Daehli, he said: "Out of respect to other clubs I don't think I can speak too much about them.
"There are other names as well. We'll announce something if something happens."