David Cameron has insisted the UK's relationship with Saudi Arabia is important for security but said "we need to look very carefully" at the education programmes funded by the Gulf State.
The Prime Minister defended the UK's ties with Riyadh but acknowledged that there were concerns about the funding for schools around the world that could "incubate a sense that one religion is right and another one is wrong".
Mr Cameron also insisted that British military personnel working with the Saudis on the controversial bombing campaign in Yemen were trying to ensure that their efforts were "properly targeted".
Asked whether there was a link between extremism in the UK and money from Saudi Arabia, the Prime Minister told BBC Radio 4's Today programme: "We do need to look at where money... it is already illegal for anyone to fund extremist groups in our country. We ban, proscribe, extremist groups.
"I think there are deeper connections where you see what is being taught in schools - not perhaps always here but around the world - and the money that is funding those educational materials.
"That's a conversation that's starting to happen."
He added: "I think if you look at what Saudi Arabia is doing, they have a good programme for deradicalising people who have become radicalised and terrorists."
"But if at the same time, money from states is funding educational programmes that can incubate a sense that one religion is right and another one is wrong, and anti-Semitic materials and what have you, then we need to look very carefully at that and that is exactly what we are doing.
"I think Saudi Arabia and other countries know that is an area they need to look at."
The UK is a major arms supplier to Saudi Arabia and it has been reported that British military personnel have been in the control room when strikes were launched by Saudi Arabia in Yemen.
But Mr Cameron defended the close ties, saying: "Our relationship with Saudi Arabia is important for our own security. They are opponents of Daesh (Islamic State) and this extremist terrorism that is causing so much damage in our world.
"When it comes to Yemen, we support the legitimate government of Yemen and work with others in order to try and help that country have the stability that it needs.
"In terms of our arms exports, we have some of the most stringent controls anywhere in the world and I will always make sure those controls are properly operated."
Saudi raids have been blamed for causing civilian casualties and striking a hospital run by Medecins Sans Frontieres.
But Mr Cameron said: "We are trying to do everything we can to make sure that the work done by Saudi Arabia is properly targeted and that is right that we should do that."
"We are working with them and others, a) on behalf of the legitimate government in Yemen, but b) what we are always doing is trying to encourage a political process in Yemen, because at the end of the day what we need in Yemen is a government that can represent every part of that country.
"There is no military solution in Yemen, at the end of the day the parties have got to come together as they are now beginning to do so, and that is very much under the pressure that Britain has put on."