"We have made a non-binding offer for Alitalia. As the largest airline in Italy, it's important we are involved in the process," Ryanair said in a statement after Italian media said on Friday that about ten such bids had been made.
The announcement comes as Ryanair on Monday logged soaring quarterly profits, aided by the timing of Easter, although the company noted that the outlook was clouded by Brexit.
British airline EasyJet, meanwhile, is believed to be among the companies to have shown an interest in taking over Alitalia, whose deadline for receiving non-binding offers had been last Friday.
Alitalia, which has struggled to compete with low-cost rivals including Ryanair, went into administration at the start of May, moving the flagship airline a step closer to liquidation as efforts continue to find a buyer.
About 18 companies expressing an interest in a potential purchase had reportedly been given access to the company's figures, including also Delta Airlines, British Airways and Lufthansa.
Italy's government in May said it would provide a bridging loan to keep Alitalia planes flying for around six months.
Those interested in making binding offers have until October.
If no buyer can be found, the administrators will have to organise Alitalia's winding-up, with the potential loss of 20,000 jobs at the company and among suppliers.