The former England youth international finished last season between the sticks for the Dolly Blues after signing in January.
Anderson’s arrival plugged a problem position considering the club ended up using nine goalkeepers during the campaign – utilising the loan market.
Fell is eager that there won’t be a repeat of that scenario next season and wants to nail down a permanent No.1.
Having produced some fine performances for City, the 21-year-old is the man in possession of the No.1 jersey and is Fell keen to see it stay that way.
However, his displays coupled with his undoubted pedigree means that there is likely to be interest in him from other clubs.
Fell said that the time is fast approaching for Anderson to make a decision on whether his immediate future lies at City or elsewhere.
"With regards to goalkeepers we have two or three options,” said Fell.
"It will not be a loan goalkeeper next season. We have learned from that last season and so it won’t be loan a keeper. The first choice is Curtis at the moment.
"He has to decide what he wants to do and we have given him a deadline.
"We do need to make a decision on that because if Curtis is going to move on, we need to activate the other options that we have got.
"I would hope by the end of this month, bearing in mind we don’t return for pre-season training until June 25, that we will have the goalkeeper situation sorted.
"If it’s not going to be Curtis, it will be someone as good and who we will be comfortable and happy with.”
Anderson played for England youth at all levels from Under-16s to the Under-19s.
He was between the sticks when the young Three Lions won the Under-17s World Cup, beating Spain in the final in 2017.
He was also part of the squad which finished runners-up in the Under-17s European Championships.
Meanwhile, City sprung a surprise with the news that long-serving duo Simon Wills and Ben Hudson will leave the club this summer.
Former captain Wills had played more than over 300 times for the Dolly Blues but following discussions with boss Mark Fell, Wills requested that the extension option wasn’t activated due to his availability and the extended travel requirements for the upcoming season.
Hudson has been at Giant Axe for a more than a decade and went on to play more than 200 games for the club in total.
However, he has decided to seek pastures new for regular first-team football
“These lads have been fantastic to work with, they’ve given their all for the club and will be remembered for their dedication and commitment to City,” said Fell.
City have though activated clauses in the contracts for Andrew Teague, Niall Cowperthwaite and Liam Brockbank for next season.