Former Scotland under-21 international Doohan was linked with a loan move to Rovers last weekend, with Scottish side St Johnstone also said to be keen on the stopper who spent last season on loan at Tranmere Rovers in League Two.
But boss Gary McSheffrey is not thought to be in the market for a goalkeeper presently.
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Three goalkeepers are currently on Doncaster’s books – Jonathan Mitchell, Louis Jones and second-year pro Ben Bottomley.
The club took up options on new contracts for Jones and Bottomley in May, while Mitchell joined on an 18-month deal in January and has since made 18 appearances.
Jones also made 16 appearances in all competitions last term.
“It’s a good mix,” new Rovers goalkeeper coach Ian Bennett said of the trio.
“The good thing about them is they are all willing to learn, they’re willing to push each other and they want to be successful for Doncaster Rovers.”
McSheffrey has already added midfielders Harrison Biggins and Luke Molyneux to his squad this summer as well as striker George Miller.
Strikers Joe Dodoo and Jordy Hiwula have both left the club.
The two-year contract Dodoo signed last summer was cancelled by mutual consent last week, while Hiwula has joined Scottish Premiership side Ross County for a nominal fee.
Doncaster currently have 21 players under contract for next season, which gets underway on Saturday 30 July when they take on Bradford City away.
Rovers still need a left back and McSheffrey is likely to utilise the loan market to further bolster his attacking options.