Cook, who averaged 24.60 during the 5-0 Ashes whitewash in Australia over the winter, hit his first century in a county game for Essex since making 154 for England against Australia A last November.
According to the BBC, Cook said that it is an exciting time for English cricket as for the first time in a long time, there have been quite a few places up for grabs, adding that it happened as they lost five consecutive Tests 'pretty heavily'.
Along with Cook, Ian Bell and their Sam Robson also made tons for their counties this week in the County Championship while fellow Test hopeful and team-mate Eoin Morgan struck 86.
Stating that good performances in the County Championship over the next few months will push the players' claims for the vacant Test places, Cook also said that he is not ruling anyone out, himself included, adding that it is nice to play and make a sizeable contribution.
The Tests against Sri Lanka take place at Lord's, from 12-16 June, and Headingley, from 20-24 June, the report added.