No, it is not possible to change content ownership without administrative privileges in ArcGIS Online. Optionally, use one of the workarounds described below to share and utilize content within an organization.
Create groups to organize specific data
In ArcGIS Online, groups can be created to allow organization members to share and contribute items. A group owner can edit properties, manage content, and change group settings. Additionally, group owners can also set a request requirement before an organization member is allowed to join the group, to permit only selected members.
Export the data from ArcGIS Online
Exporting the data from ArcGIS Online permits organization members to make an individual copy of the data to a local machine. Exporting data to the local machine gives members the authority to edit, share, and publish the data.
Copy content using ArcGIS API for Python
This option applies to organizations with more than one ArcGIS Online account. Organization members with privileges can copy content from the Operations Dashboard of their ArcGIS Online account to another by utilizing ArcGIS API for Python. Making a copy of the content in different accounts enables the organization to gatekeep private and confidential items that are not authorized for sharing with anyone other than the parties concerned.