The burly player quit as skipper and retired from one-day cricket after Pakistan's humiliating first-round exit from the World Cup in the Caribbean in March.
"I have offers from league clubs in England but I want to play for a county to ascertain my form and fitness for a place in the Pakistan Test team," said Inzamam.
Inzamam said he was training and played a full match on Sunday.
"I am training hard and am fit. I played a one-day match at the weekend and will continue my efforts to get into the Test side," said Inzamam.
Pakistan selectors have said Inzamam, who is not known for his athleticism, will have to prove his fitness to get a place in the home series against South Africa in late September this year.
But there are no domestic matches in Pakistan in between, meaning that Inzamam is looking towards England.
"I have been in touch with people and if there is a place vacant in the county I would definitely like to go and play," said Inzamam, who played 119 Tests and 378 one-day matches in a career spanning more than 16 years.
He needs just 20 runs to beat Javed Miandad's 8,832 in 124 Tests as the leading Test scorer for Pakistan.
The country's chief selector Salahuddin Ahmed has said Inzamam was not included in a list of 30 players among whom 20 will get central contracts from the Pakistan Cricket Board.
"Since Inzamam is not playing in both forms of the game we have not included him in the list for central contracts -- but the doors of Test cricket are open for him," Ahmed said last week.
Inzamam's decision to stand down as captain was prompted by Pakistan's defeat by minnows Ireland, which forced them out of the World Cup held in March and April this year.