No, there is no setting for that in Android. If you had both AP's on the same SSID, the Note 3 would eventually switch while roaming from one AP to another. It will always look for the strongest signal, but on the same SSID. I have 7 WAP's (D-Link DAP2553) setup in my home, and a Fortigate 60C firewall, so all WiFi is handled by the AP's only. I am talking from experience.
The only way the phone will switch from one SSID to another - is if the SSID visibility it's on becomes completely invisible to the phone and the phone sees the next SSID. It's hardly a practical solution.
That said, I would agree with others here that your AP /Routers are so old, they're not worth the effort. You could for a few hundred dollars, change to a single unit today that would give you far greater range and throughout, something like a D-Link Wireless AC1750 Dual-Band Gigabit Router w/ AC SmartBeam. You will get speeds up to 450 Mbps easily and range that will outperform what you have now by a huge margin. And chances are that only one of these would be needed in your home. They are under $200.00 and support 2.4/ 5 GHZ simultaneously, with guest networks / all types of security/ push button WiFi access etc. I tested one here and it has insane range and throughput. I could easily replace all 7 WAP's with 3 of these and get much faster throughput.