Ramsey is said to be visiting all the clubs interested in his signature as he dcides where to go.
We would prefer it if Aaron signed for Manchester United, to be honest," said Ridsdale.
"The simple reason being that, from our perspective, we want him to come back to Cardiff next season.
"I am sure that is something which all our supporters will be hoping for as well."
Dave Jones believes Ramsey has it in him to make the grade at Old Trafford.
We have no doubts whatsoever that Aaron could make the grade at somewhere like Manchester United," Jones said
"We would not let him go there if we had any doubts.
"United are the major force in European football, if not the best club in the world, and with the squad of players they have that domination is set to continue for some time to come.
"I believe Aaron can go there and play a valuable part in that in the future."