The prolific striker is hopeful of recovering from knee surgery in time to represent Uruguay at the World Cup in Brazil next month.
While a number of Gerrard's Liverpool teammates, including Jordan Henderson and Glen Johnson, have revealed that they have been in contact with Suarez, the Three Lions skipper is purely focused on England.
"I don't know whether [Suarez] is going to be available. For me, it's not very important. It's something that we can't control. It's not my main focus."
England will play Uruguay in Group D in Sao Paulo on June 19.