Fabianski has had a terrific first season at Swansea after leaving Arsenal on a free transfer last season and has a chance to win the Barclays Premier League's Golden Glove award on the final day of the season at Crystal Palace.
But Fabianski's form is said to have alerted Dortmund and led to speculation that the 30-year-old Pole could be offered a new improved contract to keep him at Swansea.
"We can easily keep him (Fabianski) here," Monk said
"He's a Swansea City player and very committed to this club.
"We've given him a great opportunity which he wanted, he's fought for this chance and deserved it.
"He's earned the right to have that opportunity, but players see the club going forward and they sense it every day.
"There's no reason to move and the conversations I've had with them tells me they are very much looking forward to next season."
It has been reported that Fabianski's representatives have already held talks with Swansea over new terms but Monk said he was "unaware" this was the case, with the player still having three years to run on the deal he signed last summer.
"Whether his agents are discussing, or trying to discuss, with the club I'm not sure what level that's at," Monk said.
"It's a possibility his agents have made contact with the club but I'm unaware of it.
"We'll see in the future about the negotiations but the reward will come if the club sees fit and I'll have those conversations with the chairman.
"There's an element that these players are lucky to play for this club and the level that they are.
"They've got a great platform at a club which is progressive and to be in a team that has done remarkably well this season.
"It's about them fighting for that opportunity as well, so it's a two-way thing, and it's important they show loyalty."
Fabianski struggled to make his mark in seven seasons at Arsenal, making only 32 league appearances in that time and eventually finding himself the back-up goalkeeper to his fellow Pole, Wojciech Szczesny.
But since joining Swansea he has reclaimed the Poland number one jersey from Szczesny and kept 13 Premier League clean sheets, the joint-highest along with Joe Hart, Simon Mignolet, Ben Foster and Fraser Forster.
That means Fabianski goes into the final game of the season on Sunday with a chance of winning the Golden Glove.
"It would be great to keep that clean sheet and give him a chance to do it," Monk said.
"I'm sure Lukasz is thinking about that as well as the team and it's one of the objectives this weekend.
"Hopefully we can do it and cap off a good season from him and the team.
"It would be a boost for everyone and a pointer that we're going in the right direction, and that we made the right decision to bring him in last summer and show everyone what a fantastic player he is."
Source : PA
Source: PA