The 38-year-old left the San Siro at the end of the season after an 11-year spell with the Serie A giant.
Reports had suggested Inzaghi's next move could be to the
"I know exactly where that has come from," he told the
"I was sat in
"We were introduced to an Italian agent and we said hello.
"We started talking about numerous players and he said: 'I can get you Inzaghi'.
"I said: 'Okay, that's good, he's old isn't he?'
"I told him that we wouldn't be going down that road and I was happy with the players that I have and we carried on talking.
"That translated as 'we've offered him a contract worth about £960,000'."
McDermott did, though, reveal that veteran midfielder Brynjar Gunnarsson will be offered a new contract.
The 36-year-old is set to sign a new deal with the Royals and is likely to be named in the 25-man Premier League squad.
"He will definitely get something at this football club," McDermott said.
"My gut feeling is that he will be in the 25-man squad too.
"If you look at the numbers, right now we're up to 23.
English Premier League