Discussions with Sinclair, who is out of contract at the Liberty Stadium next summer, were put on hold following the departure of former boss Brendan Rodgers to Liverpool last month.
The 23-year-old, who joined the Swans from Chelsea two years ago, was keen to speak with Rodgers' successor before making any decision on his future, according to Jenkins.
And the chairman says Swansea will hold more talks with the winger following Laudrup's appointment last week.
"Scott's position was delayed somewhat until we appointed a new manager," Jenkins told the South Wales Evening Post.
"I think that was important, to make sure the new manager had a chance to speak to Scott himself, whatever we decided to do.
"Whether you put him on a long contract or not, I think it should be a joint process to make sure the manager is fully involved.
"And over the next few weeks, prior to the start of pre-season, we'll sit down with Scott and discuss his feelings.
"I spoke to Scott and his agent prior to Brendan leaving.
"Scott was waiting to see who we appointed as manager, and then to speak to the manager."