Darrell Clarke's side clinched third in League Two with a last-gasp winner on Saturday against Dagenham & Redbridge.
New Zealand forward Rory Fallon, 34, is to be released after making just three first-team appearances this season.
Defenders Lee Brown, scorer of the late winner over Dagenham, and Tom Lockyer already signed new contracts in April.
Having secured back-to-back promotions, securing top scorer Matty Taylor's services for at least another season would be seen as a major boost for the club if he was to agree a new deal.
After Saturday's victory, the striker told BBC Radio Bristol he would speak to club's president regarding a new deal.
Chairman Steve Hamer has said the club will have the chance to match offers made by other clubs for Taylor this summer.

The government has granted planning permission for the 15-year project including new stages and streetscapes at the site in Iver Heath.
South Bucks District Council (SBDC), which turned down the "inappropriate" plans, said it was "disappointed".
The latest Star Wars film, Episode VII, is currently being filmed at Pinewood.
It has been home to more than 1,500 movies over 76 years including the most recent James Bond movie, Skyfall.
The expansion project, known as the Pinewood Studios Development Framework (PSDF), will double the existing studios by adding a total of 100,000 square metres of new facilities, including 12 large stages, workshops and production offices.
A studio spokesman said the expansion would "secure future growth".
The studio said the decision by the Secretary of State for Communities and Local Government, Eric Pickles, "will address the clear need for additional capacity in the UK".
Pinewood chief executive Ivan Dunleavy said: "We want to begin construction as soon as possible."
In 2012, the government rejected a previous plan, which included more than 1,000 homes.
The studio submitted its latest application in February 2013, following "extensive public consultation".
It was rejected by the local council and the studios submitted its appeal to the Planning Inspectorate the following May.
Nearby councils have always opposed the plans as an expansion into green belt land.
Councillor Roger Reed said SBDC had presented "extensive and well informed objections".
"We must now look forward and recognise the importance of Pinewood and the benefit they can bring to the local and wider economy," he added.
Parish councillor Sylvie Lowe, who represents Iver, said she was "surprised" at the decision and the council was considering its options.

The MAC chief executive Anne McReynolds was speaking ahead of a debate at the theatre later that involves members of the main political parties.
She said the arts benefit the economy.
"Our politicians understand the arts contribute to wider society in terms of economic renewal, cultural tourism and social regeneration," she said.
"The arts are an economic driver in Northern Ireland and yet we're languishing at the bottom of the levels of subsidy and investment compared to other parts of the UK."
A number of Northern Ireland arts organisations face funding cuts amid pressures on the Stormont budget.
Promoted Bristol Rovers have offered new contracts to all but one of their senior professional players after their dramatic finish to the league season.
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Pinewood Studios is set to double in size after winning an appeal against the rejection of its £200m expansion plan.
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A theatre manager in Belfast has questioned why the arts in Northern Ireland receives less funding than other parts of the UK.