The trio, who all played differing roles in Cherries' momentous League Two promotion, were offered new one-year contracts during post-season meetings with Howe yesterday.
Striker Fletcher and winger McQuoid both featured regularly as Cherries secured a place in League One, while Cooper only returned last month following a long layoff.
However, despite being sidelined for much of the season, gifted playmaker Cooper will be a key member of Howe's squad as Cherries look to bridge the step up in class.
Warren Cummings, Lee Bradbury and Danny Hollands are also weighing up their options after triggering appearance-related clauses in their existing deals.
And while they are automatically entitled to fresh terms, they could still leave should they receive better offers, although Bradbury and Cummings have already indicated they will stay.
However, Sammy Igoe, Scottie Guyett and Jeff Goulding, who all suffered injury-plagued campaigns, were not offered fresh terms when they met Howe.
Meanwhile, boss Howe confirmed that talks were ongoing with striker Alan Connell, the 10th member of the Cherries squad whose contract is due to expire at the end of next month.
Discussing yesterday's developments, Howe told the Daily Echo: It is a difficult process but one which has to be carried out. There is a lot to consider, particularly this season following promotion.
The decisions are not rash or based on two or three games. A lot of thought has gone into our plans for next season and beyond. We are hoping to tie up deals with Shaun Cooper, Steve Fletcher and Josh McQuoid having offered them something. We see them all as an important part of the future.
The three lads with options have all been offered the appropriate terms in relation to the clauses in their respective contracts and we await their decisions.
Scottie, Sammy and Jeff all played their part in a successful season so it was a very difficult decision not to offer them something.
They have all suffered with injuries, which has probably been hard for them. Jeff had a really good pre-season and, unfortunately, got injured just after the start.
Sammy started the season in great form and then picked up a nasty injury. Scottie was injured for a large part and had to have a couple of operations. Injuries played a part in their seasons and they have been unfortunate. We would like to publically thank them for their service to the club and wish them all the best for the future. They are excellent professionals and have been a pleasure to work with.
Howe is expected to add to his squad by also offering terms to youth team graduates Dan Thomas, Tim Stephenson and Danny Ings.