Former Barcelona playmaker Orlandi, 26, signed a one-year contract extension to remain with the Swans until the summer of 2013, following in the footsteps of compatriot Rangel, who agreed a three-year deal last week.
"Improving and extending certain players' contracts well in advance is something we can now look into thanks to our Premier League status," said Jenkins.
"Over the last few years we have been asked by supporters why the club did not do it, but the simple explanation is we were not in a financial position to do so.
"The budget was set to compete in the Championship, so any further money spent on securing certain players' contracts earlier would have jeopardised certain signings along the way. An example of that is Fabio Borini. We budgeted well and that allowed us to add a quality player like Fabio to the team for the final push.
"I think it is important to explain this to everyone connected with the club, so we are all on the same page. So we will be looking to sit down with the likes of Joe Allen, Nathan Dyer and Jazz Richards, for example, and ensure their contracts and cover our assets in advance.''
Jenkins was delighted to see Orlandi remain in south Wales, but has quelled rumours that the club are close to signing Ghana defender Isaac Vorsah and Barcelona B forward Jonathan Soriano. Jenkins headed to the continent last week in an effort to secure additional squad reinforcements. The Swans have so far only added striker Danny Graham to their squad for a club-record fee of £3.5million.
Jenkins distanced the club from a move for Hoffenheim centre-back Vorsah, saying: "Swansea City would like to confirm that there is no truth in this rumour."
He added that while Swansea were interested in the highly-rated Soriano, who scored 32 goals last season, they had not been able to agree terms.`
"We were prepared to offer the player an opportunity to join our squad in our first season in the Premier League, but we were not happy with the terms of the deal to suit Swansea City Football Club. We continue to look at all of our options," said Jenkins.
Source: PA
Source: PA