Ethernet interface no sleep at all times

i am hibernating / sleeping my pc after 10 min. while in hibernation I can see that the ethernet interface port LEDs are not on or blinking as an indication for "on" or standby mode. How to prevent the ethernet interface to sleep at all times in ubuntu? My main goal is to utilize the WoL feature to wake up my PC remotely. Some information:

$ sudo lshw -C network
*-network
description: Ethernet interface
product: RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller
vendor: Realtek Semiconductor Co., Ltd.
physical id: 0
bus info: [email protected]:04:00.0
logical name: enp4s0
version: 06
serial: XX:XX:XX:XX:XX:XX
size: 100Mbit/s
capacity: 1Gbit/s
width: 64 bits
clock: 33MHz
capabilities: pm msi pciexpress msix vpd bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation
configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl_nic/rtl8168e-2.fw ip=XXX.XXX.XXX.XXX latency=0 link=yes multicast=yes port=MII speed=100Mbit/s
resources: irq:18 ioport:d000(size=256) memory:ec104000-ec104fff memory:ec100000-ec103fff
#############################

$ ifconfig -a
enp4s0: flags=4163<UP,BROADCAST,RUNNING,MULTICAST> mtu 1500
inet XXX.XXX.XXX.XXX netmask XXX.XXX.XXX.X broadcast XXX.XXX.XXX.XXX
inet6 XXXX::XXXX:XXXX:XXXX:XXXX prefixlen 64 scopeid 0x20
ether XX:XX:XX:XX:XX:XX txqueuelen 1000 (Ethernet)
RX packets 105479 bytes 15854955 (15.8 MB)
RX errors 0 dropped 0 overruns 0 frame 0
TX packets 11389 bytes 1383817 (1.3 MB)
TX errors 0 dropped 0 overruns 0 carrier 0 collisions 0

lo: flags=73<UP,LOOPBACK,RUNNING> mtu 65536
inet 127.0.0.1 netmask 255.0.0.0
inet6 ::1 prefixlen 128 scopeid 0x10
loop txqueuelen 1000 (Local Loopback)
RX packets 2284 bytes 237460 (237.4 KB)
RX errors 0 dropped 0 overruns 0 frame 0
TX packets 2284 bytes 237460 (237.4 KB)
TX errors 0 dropped 0 overruns 0 carrier 0 collisions 0

###########

$ sudo ethtool enp4s0
Settings for enp4s0:
Supported ports: [ TP MII ]
Supported link modes: 10baseT/Half 10baseT/Full
100baseT/Half 100baseT/Full
1000baseT/Half 1000baseT/Full
Supported pause frame use: No
Supports auto-negotiation: Yes
Supported FEC modes: Not reported
Advertised link modes: 10baseT/Half 10baseT/Full
100baseT/Half 100baseT/Full
1000baseT/Half 1000baseT/Full
Advertised pause frame use: Symmetric Receive-only
Advertised auto-negotiation: Yes
Advertised FEC modes: Not reported
Link partner advertised link modes: 10baseT/Half 10baseT/Full
100baseT/Half 100baseT/Full
Link partner advertised pause frame use: Symmetric Receive-only
Link partner advertised auto-negotiation: Yes
Link partner advertised FEC modes: Not reported
Speed: 100Mb/s
Duplex: Full
Port: MII
PHYAD: 0
Transceiver: internal
Auto-negotiation: on
Supports Wake-on: pumbg
Wake-on: g
Current message level: 0x00000033 (51)
drv probe ifdown ifup
Link detected: yes

Follow up -- additional information: I can inform that when the pc is in normal operation the two LEDs at the network interface are blinking. When the pc is in sleep/hibernation mode, the LEDs are off.