Reds considering bids for club extremely carefully...
The Reds are still under the control of American co-owners Tom Hicks and George Gillett, but chairman Martin Broughton is on a mission to find the Americans' successors.
"We have had a number of bids for the club. We will take time to examine those extremely carefully," Purslow told BBC Radio 5 Live's 'Sportsweek' programme.
"Second to that is [the need] to sell the club as soon as possible."
Purslow insists that securing the right buyer - either Chinese businessman Kenny Huang or Canadian-based Syrian Yahya Kirdi, who are reportedly among the interested parties - will be of greater importance than accepting the quickest solution.
"We will make sure we take our time," he continued.
"I am not going to put a time limit on it. The challenge now is to sort the wheat from the chaff. I would not expect it to be a lifetime - but I would not expect it to be tomorrow either.
"We have just received some written bids at this stage, and it would be wrong to characterise anybody as a front-runner."
Having finished a disappointing seventh in the Premier League last season, the Merseyside outfit have been boosted this summer by the appointment of Roy Hodgson as manager, the arrival of Joe Cole and the news that key players including Steven Gerrard and Fernando Torres were committing themselves to the club.
Ahead of their opening game of the new campaign, against Arsenal at Anfield this afternoon, Purslow has outlined the expectations around the club for the forthcoming season.
"The target is significant improvement. We think our club and players belong in the Champions League - so that is where we would like to be," he said.
"I think there will be one or two more ins and outs. There are a few people who will move on. Javier [Mascherano] has been wanting to go for personal reasons.
"We have not had any offers for him, and the manager is very happy with him. But it is true he is looking for a move."